Articles | Volume 9, issue 3/4
https://doi.org/10.5194/npg-9-221-2002
© Author(s) 2002. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.
https://doi.org/10.5194/npg-9-221-2002
© Author(s) 2002. This work is licensed under
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.
the Creative Commons Attribution-NonCommercial-ShareAlike 2.5 License.
Higher-order Korteweg-de Vries models for internal solitary waves in a stratified shear flow with a free surface
R. Grimshaw
Department of Mathematical Sciences, Loughborough University, Loughborough, UK
E. Pelinovsky
Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics and Department of Applied Mathematics, Nizhny Novgorod Technical University, Nizhny Novgorod, Russia
O. Poloukhina
Laboratory of Hydrophysics and Nonlinear Acoustics, Institute of Applied Physics and Department of Applied Mathematics, Nizhny Novgorod Technical University, Nizhny Novgorod, Russia
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98 citations as recorded by crossref.
- Breather generation in fully nonlinear models of a stratified fluid K. Lamb et al. 10.1103/PhysRevE.75.046306
- Simulation of the Transformation of Internal Solitary Waves on Oceanic Shelves R. Grimshaw et al. 10.1175/JPO2652.1
- DECOUPLED AND UNIDIRECTIONAL ASYMPTOTIC MODELS FOR THE PROPAGATION OF INTERNAL WAVES V. DUCHÊNE 10.1142/S0218202513500462
- Internal Wave Breathers in the Slightly Stratified Fluid T. Talipova et al. 10.1007/s12217-019-09738-2
- Residual Symmetries and Interaction Solutions for the Classical Korteweg-de Vries Equation J. Fei et al. 10.1515/zna-2016-0339
- Soliton molecules and asymmetric solitons in three fifth order systems via velocity resonance S. Lou 10.1088/2399-6528/ab833e
- Soliton solutions to the fifth-order Korteweg–de Vries equation and their applications to surface and internal water waves K. Khusnutdinova et al. 10.1063/1.5009965
- Discussion on the extended form of internal solitary wave models between two typical stratification systems J. Zhang et al. 10.1007/s42241-023-0002-6
- Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea Z. Xu et al. 10.1007/s00343-010-9018-1
- Beyond the KdV: Post-explosion development L. Ostrovsky et al. 10.1063/1.4927448
- Observations of Shoaling Nonlinear Internal Bores across the Central California Inner Shelf J. McSweeney et al. 10.1175/JPO-D-19-0125.1
- Exact solitary wave solutions for a coupled gKdV–Schrödinger system by a new ODE reduction method S. Anco et al. 10.1111/sapm.12768
- A fifth-order variable coefficient KdV equation arising from a fluid system Z. Yu & M. Jia 10.1088/1402-4896/ac15c4
- Modeling of long nonlinear waves on the interface in a horizontal two-layer viscous channel flow D. Arkhipov & G. Khabakhpashev 10.1007/s10697-005-0051-2
- Effects of tidal currents on nonlinear internal solitary waves in the South China Sea Z. Fan et al. 10.1007/s11802-013-1870-0
- Soliton molecules and few-cycle-pulse solitons structures for the generalized Konopelchenko–Dubrovsky–Kaup–Kupershmidt equation M. Jia 10.1007/s11071-023-08899-5
- Internal solitons in the ocean and their effect on underwater sound J. Apel et al. 10.1121/1.2395914
- Novel soliton molecules and interaction wave solutions in a (2+1)-dimensional Sawada–Kotera equation: a multi-linear variable separation method J. Sun et al. 10.1007/s11071-023-08485-9
- On the Rigid-Lid Approximation for Two Shallow Layers of Immiscible Fluids with Small Density Contrast V. Duchêne 10.1007/s00332-014-9200-2
- Localization of nonlocal symmetries and interaction solutions of the Sawada–Kotera equation J. Wu et al. 10.1088/1572-9494/abf552
- Nonlocal symmetries and explicit solutions for the Gardner equation J. Fei et al. 10.1016/j.amc.2017.07.002
- Seasonal Variability and Generation Mechanisms of Nonlinear Internal Waves in the Strait of Georgia L. Li et al. 10.1029/2017JC013563
- Marine seismic observation of internal solitary wave packets in the northeast South China Sea Q. Tang et al. 10.1002/2015JC011362
- Distribution of vertical turbulent mixing parameter caused by internal tidal waves and solitary waves in the South Yellow Sea Z. Si et al. 10.1007/s11802-012-1910-1
- Effects of topography and Earth's rotation on the oblique interaction of internal solitary‐like waves in the Andaman Sea K. Shimizu & K. Nakayama 10.1002/2017JC012888
- Perturbative and reversible systems approaches to new families of embedded solitary waves of a generalized fifth-order Korteweg–de Vries equation S. Choudhury & R. Alfonso Rodriguez 10.1016/j.padiff.2022.100314
- Internal solitary waves shoaling onto a shelf: Comparisons of weakly-nonlinear and fully nonlinear models for hyperbolic-tangent stratifications K. Lamb & W. Xiao 10.1016/j.ocemod.2014.02.005
- Propagation regimes of interfacial solitary waves in a three-layer fluid O. Kurkina et al. 10.5194/npg-22-117-2015
- New exact traveling wave solutions of the unstable nonlinear Schrödinger equations and their applications Y. Li et al. 10.1016/j.ijleo.2020.165386
- Multi-soliton solutions of the forced variable-coefficient extended Korteweg–de Vries equation arisen in fluid dynamics of internal solitary waves Y. Liu et al. 10.1007/s11071-010-9936-7
- Group classification of linear evolution equations A. Bihlo & R. Popovych 10.1016/j.jmaa.2016.11.020
- Nonlinear Waves in a Rotating Ocean (The Ostrovsky Equation and Its Generalizations and Applications) Y. Stepanyants 10.1134/S0001433820010077
- Bilinear Bäcklund transformation, Lax pair, Darboux transformation, multi-soliton, periodic wave, complexiton, higher-order breather and rogue wave for geophysical Boussinesq equation N. Pal et al. 10.1007/s12043-024-02773-8
- Exact solutions for the nonlinear extended KdV equation in a stratified shear flow using modified exponential rational method A. Althobaiti et al. 10.1016/j.rinp.2021.104723
- Painlevé analysis, Lax pair, Bäcklund transformation and multi-soliton solutions for a generalized variable-coefficient KdV–mKdV equation in fluids and plasmas G. Meng et al. 10.1088/0031-8949/85/05/055010
- Pulse wave propagation in a deformable artery filled with blood: an analysis of the fifth-order mKdV equation with variable coefficients Y. Yang et al. 10.1080/17455030.2021.1950948
- Spatiotemporal variations of parameters of internal solitary waves in the northern South China Sea Y. Liu et al. 10.1007/s00343-023-3025-5
- Regional study of mode-2 internal solitary waves at the Pacific coast of Central America using marine seismic survey data W. Fan et al. 10.5194/npg-29-141-2022
- The derivation of an isotropic model for internal waves and its application to wave generation C. Yuan et al. 10.1016/j.ocemod.2020.101663
- M-shaped rational, homoclinic breather, kink-cross rational, multi-wave and interactional soliton solutions to the fifth-order Sawada-Kotera equation S. Baloch et al. 10.1016/j.padiff.2024.100919
- Multi-soliton solutions, breather-like and bound-state solitons for complex modified Korteweg–de Vries equation in optical fibers Z. Lan 兰 10.1088/1674-1056/ad39d7
- Travelling wave solutions on a non-zero background for the generalized Korteweg–de Vries equation S. Anco et al. 10.1088/1751-8121/abda77
- Impacts of a Mesoscale Eddy Pair on Internal Solitary Waves in the Northern South China Sea revealed by Mooring Array Observations X. Huang et al. 10.1175/JPO-D-16-0111.1
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- A nonhydrostatic oceanic regional model, ORCTM v1, for internal solitary wave simulation H. Huang et al. 10.5194/gmd-16-109-2023
- Generation of large-amplitude solitons in the extended Korteweg–de Vries equation R. Grimshaw et al. 10.1063/1.1521391
- Abundant Traveling Wave Structures of (1+1)-Dimensional Sawada-Kotera Equation: Few Cycle Solitons and Soliton Molecules* W. Wang et al. 10.1088/0256-307X/37/10/100501
- Nonlinear interaction of internal and surface gravity waves in a two-layer fluid with free surface I. Selezov et al. 10.1007/s10958-010-0010-2
- Higher-order (2 + 4) Korteweg-de Vries-like equation for interfacial waves in a symmetric three-layer fluid O. Kurkina et al. 10.1063/1.3657816
- A high-order nonlinear Boussinesq-type model for internal waves over a mildly-sloping topography in a two-fluid system Z. Liu et al. 10.1016/j.oceaneng.2023.115283
- Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea K. Lamb & A. Warn-Varnas 10.5194/npg-22-289-2015
- Novel travelling wave structures for (2+1)-dimensional Sawada–Kotera equation X. Wang et al. 10.1016/j.aml.2021.107638
- Asymptotics of solutions to a fifth-order modified Korteweg–de Vries equation in the quarter plane N. Liu & B. Guo 10.1142/S0219530519500210
- Modulation instability of long internal waves with moderate amplitudes in a stratified horizontally inhomogeneous ocean T. Talipova et al. 10.1134/S0021364011150124
- Exact Travelling-Wave Solutions of the Extended Fifth-Order Korteweg-de Vries Equation via Simple Equations Method (SEsM): The Case of Two Simple Equations E. Nikolova 10.3390/e24091288
- High-level Green–Naghdi model for large-amplitude internal waves in deep water B. Zhao et al. 10.1017/jfm.2024.460
- Lie group analysis and novel solutions for the generalized variable-coefficients Sawada-Kotera equation R. El-Shiekh & M. Gaballah 10.1209/0295-5075/acb460
- Bidirectional Whitham type equations for internal waves with variable topography C. Yuan & Z. Wang 10.1016/j.oceaneng.2022.111600
- Diverging probability-density functions for flat-top solitary waves A. Peleg et al. 10.1103/PhysRevE.80.026602
- Analytical solutions of long nonlinear internal waves: Part I S. Hamdi et al. 10.1007/s11069-011-9757-0
- (3+1)-Dimensional Gardner Equation Deformed from (1+1)-Dimensional Gardner Equation and its Conservation Laws G. Jin et al. 10.1051/mmnp/2024004
- Nonlinear internal wave packets in shelf zone . Макаренко et al. 10.25743/ICT.2019.24.2.008
- Alongshore Variability of Shoaling Internal Bores on the Inner Shelf J. McSweeney et al. 10.1175/JPO-D-20-0090.1
- On the vertical structure of internal solitary waves in the northeastern South China Sea Y. Gong et al. 10.1016/j.dsr.2021.103550
- Analysis of the rogue waves in the blood based on the high-order NLS equations with variable coefficients* Y. Yang et al. 10.1088/1674-1056/abff31
- Conservation laws and invariants of motion for nonlinear internal waves: part II S. Hamdi et al. 10.1007/s11069-011-9737-4
- Riemann-Hilbert method and multi-soliton solutions of an extended modified Korteweg-de Vries equation with N distinct arbitrary-order poles J. Yang et al. 10.1016/j.jmaa.2022.126103
- Undular bores generated by fracture C. Hooper et al. 10.1103/PhysRevE.104.044207
- Longitudinal bulk strain solitons in a hyperelastic rod with quadratic and Cubic nonlinearities F. Garbuzov et al. 10.1134/S0040577920030046
- Time‐spatial variability observed in velocity of propagation of the internal bore in the Strait of Gibraltar J. Sánchez Garrido et al. 10.1029/2007JC004624
- Modelling Internal Solitary Waves in the Coastal Ocean R. Grimshaw et al. 10.1007/s10712-007-9020-0
- Stability and dynamics of regular and embedded solitons of a perturbed Fifth-order KdV equation S. Choudhury et al. 10.1016/j.physd.2024.134056
- Two-dimensional interaction of a shear flow with a free surface in a stratified fluid and its solitary-wave solutions via mathematical methods A. Seadawy 10.1140/epjp/i2017-11755-6
- An Empirical Model for Estimating the Geographic Location of Nonlinear Internal Solitary Waves C. Jackson 10.1175/2009JTECHO638.1
- Temporal variability of internal solitary waves in the northern South China Sea revealed by long-term mooring observations X. Huang et al. 10.1016/j.pocean.2021.102716
- On the stability of internal waves H. Kalisch & N. Nguyen 10.1088/1751-8113/43/49/495205
- LONG NONLINEAR INTERNAL WAVES K. Helfrich & W. Melville 10.1146/annurev.fluid.38.050304.092129
- Multisolitons in the surface gravity waves and internal waves H. Jia et al. 10.1142/S0217984923501063
- Internal waves in marginally stable abyssal stratified flows N. Makarenko et al. 10.5194/npg-25-659-2018
- Internal waves in a compressible two-layer model atmosphere: Hamiltonian description V. Ruban 10.1134/S1063776110110099
- Seasonal and spatial variations of kinematic parameters of internal solitary waves in the Andaman Sea Y. Wu et al. 10.1007/s13131-021-1854-7
- A novel (2+1)-dimensional Sawada-Kotera type system: multisoliton solution and variable separation solution J. Wang et al. 10.1007/s11071-024-09511-0
- Fractional solitary wave solutions of the nonlinear higher-order extended KdV equation in a stratified shear flow: Part I A. Seadawy 10.1016/j.camwa.2015.04.015
- Barotropic-Baroclinic Coherent-Structure Rossby Waves in Two-Layer Cylindrical Fluids J. Xu et al. 10.3390/axioms12090856
- Продольные объемные солитоны деформации в гиперупругом стержне с квадратичной и кубической нелинейностями F. Garbuzov et al. 10.4213/tmf9803
- Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion M. Hongler 10.3390/sym13010057
- Higher-Order Benjamin–Ono Model for Ocean Internal Solitary Waves and Its Related Properties Y. Ren et al. 10.3390/axioms12100969
- Symmetries, conservation laws, and line soliton solutions of a two-dimensional generalized KdV equation with $ p $-power A. Márquez et al. 10.3934/dcdss.2024130
- Physical uniqueness of higher-order Korteweg-de Vries theory for continuously stratified fluids without background shear K. Shimizu 10.1063/1.5008767
- Analytical and numerical studies of the variable-coefficient Gardner equation O. Nakoulima et al. 10.1016/S0096-3003(03)00569-1
- A multi-layer model for nonlinear internal wave propagation in shallow water P. Liu & X. Wang 10.1017/jfm.2012.24
- Oceanic internal solitary wave interactions via the KP equation in a three-layer fluid with shear flow J. Sun et al. 10.1007/s11071-024-09307-2
- Internal waves generated by explosive eruptions of underwater volcanoes and their effect on the sea surface T. Talipova et al. 10.1007/s11069-024-06851-3
- Three-Dimensional Evolution of Large-Amplitude Internal Waves in the Strait of Gibraltar V. Vlasenko et al. 10.1175/2009JPO4007.1
- The modulation of multiple phases leading to the modified Korteweg–de Vries equation D. Ratliff 10.1063/1.5037280
- Два типа волн в двухслойной стратифицированной жидкости A. Rudenko 10.26117/2079-6641-2023-43-2-111-125
- Classification of internal solitary wave breaking over a slope K. Nakayama et al. 10.1103/PhysRevFluids.4.014801
- The N-soliton molecule for the combined(2N+1)th-order Lax’s KdV equation X. Cheng et al. 10.1016/j.rinp.2020.103184
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