Effects of rotation and topography on internal solitary waves governed by the rotating Gardner equation by K. R. Helfrich, L. Ostrovsky, L. Ostrovsky

“…Here the basic model is the extended Korteweg–de Vries equation that includes both quadratic and cubic nonlinearity (the Gardner equation) with additional terms incorporating slowly varying depth and weak rotation. …”
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Soliton wave solutions of ion-acoustic waves a cold plasma with negative ions by Dexu Zhao, Dianchen Lu, Samir A Salama, Piyaphong Yongphet, Mostafa MA Khater

“…This article investigates the computational complex wave solutions of the modified Korteweg–de Vries equation combined with an adverse order of the Korteweg–de Vries model. …”
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On time relaxed schemes and formulations for dispersive wave equations by Jean-Paul Chehab, Denys Dutykh

“…In this article we illustrate the application of the new relaxed scheme on the classical Korteweg–de Vries equation as a prototype of stiFF dispersive PDEs.…”
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Solitary Wave Interactions with an External Periodic Force: The Extended Korteweg-de Vries Framework by Marcelo V. Flamarion, Efim Pelinovsky

“…In this work we asymptotically and numerically studied the interaction of large amplitude solitary waves with an external periodic force using the forced extended Korteweg-de Vries equation (feKdV). Regarding these interactions, we found three types of regimes depending on the amplitude of the solitary wave and how its speed and the speed of the external force are related. …”
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Solitary Wave Solutions for the Stochastic Fractional-Space KdV in the Sense of the M-Truncated Derivative by Wael W. Mohammed, Clemente Cesarano, Farah M. Al-Askar, Mahmoud El-Morshedy

“…The stochastic fractional-space Korteweg–de Vries equation (SFSKdVE) in the sense of the M-truncated derivative is examined in this article. …”
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Traveling wave solutions of the generalized scale-invariant analog of the KdV equation by tanh–coth method by González-Gaxiola Oswaldo, Ruiz de Chávez Juan

“…In this work, the generalized scale-invariant analog of the Korteweg–de Vries equation is studied. For the first time, the tanh–coth methodology is used to find traveling wave solutions for this nonlinear equation. …”
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Theoretical investigation of the behavior of spherical ion- acoustic solitons in two-temperature plasma by M Nezam, A Nazari Golshan

“…The obtained spherical Korteweg–de Vries equation was solved using a homotopy perturbation method (HPM). …”
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Approximate asymptotic integration of a higher order water-wave equation using the inverse scattering transform by A. R. Osborne

“…I seek to integrate the first higher-order wave equation, beyond the order of the Korteweg- deVries equation, using the inverse scattering transform. …”
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A <i>τ</i>-Symmetry Algebra of the Generalized Derivative Nonlinear Schrödinger Soliton Hierarchy with an Arbitrary Parameter by Jian-bing Zhang, Yingyin Gongye, Wen-Xiu Ma

“…The resulting hierarchies include the Kaup-Newell equation, the Chen-Lee-Liu equation, the Gerdjikov-Ivanov equation, the modified Korteweg-de Vries equation, the Sharma-Tasso-Olever equation and a new equation as special reductions. …”
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Automated Differential Equation Solver Based on the Parametric Approximation Optimization by Alexander Hvatov

“…In this paper, we provide examples of the Legendre equation, Painlevé transcendents, wave equation, heat equation, and Korteweg–de Vries equation, which are solved in a unified manner without significant changes to the algorithm’s parameters.…”
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On the oscillations in a nonextensive complex plasma by improved differential transformation method: An application to a damped Duffing equation by Noufe H Aljahdaly, Maram A Alharbi, Abrar A Alharbi, RA Alharbey, SA EL-Tantawy

“…For this purpose, the set of fluid equations of the present plasma model is reduced to the Burger-modified Korteweg De Vries equation (BmKdV) equation using a reductive perturbation technique. …”
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Solitary and periodic waves in collisionless plasmas: the Adlam-Allen model revisited by Allen, JE, Frantzeskakis, DJ, Karachalios, NI, Kevrekidis, PG, Koukouloyannis, V

“…In addition, employing a long-wave approximation via a relevant multiscale expansion method, we establish the asymptotic reduction of the AA system to the Korteweg-de Vries equation. Such a reduction is not only another justification for the above solitary wave dynamics, but may also offer additional insights for the emergence of other possible plasma waves. …”

Symbolic genetic algorithm for discovering open-form partial differential equations (SGA-PDE) by Yuntian Chen, Yingtao Luo, Qiang Liu, Hao Xu, Dongxiao Zhang

“…In the experiment, SGA-PDE not only successfully discovered the nonlinear Burgers’ equation, the Korteweg–de Vries equation, and the Chafee-Infante equation but also handled PDEs with fractional structure and compound functions that cannot be solved by conventional PDE discovery methods.…”
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Some finite difference methods for solving linear fractional KdV equation by Appanah Rao Appadu, Abey Sherif Kelil

“…The time-fractional Korteweg de Vries equation can be viewed as a generalization of the classical KdV equation. …”
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Head-on collision of ion-acoustic multi-solitons and study of rogue waves in electron-beam superthermal plasma by Sunidhi Singla, N.S. Saini

“…In this investigation, head-on collision of ion-acoustic (IA) multi-solitons and study of characteristics of ion acoustic rogue waves in an unmagnetized plasma which includes ion fluid, superthermal hot electrons, and penetrated by electron beam have been presented. The Korteweg-de Vries equation have been derived by employing the extended Poincaré-Lighthill-Kuo (PLK) method. …”
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Dynamics and exact solutions of the generalized Harry Dym equation by Ruslan Matviichuk

“…The Harry Dym equation has strong links to the Korteweg – de Vries equation and it also has many properties of soliton solutions. …”
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Rational Solitons in the Gardner-Like Models by Efim Pelinovsky, Tatiana Talipova, Ekaterina Didenkulova

“…In this work, bounded rational solutions of Gardner-type equations (the extended Korteweg-de Vries equation), when a nonlinear term can be represented as a sum of several terms with arbitrary powers (not necessarily integer ones), are found. …”
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Ion-acoustic cnoidal waves in a non-Maxwellian plasma with regularized κ-distributed electrons by Ma’mon Abu Hammad, Muhammad Khalid, Albandari W. Alrowaily, C. G. L. Tiofack, S. A. El-Tantawy

“…By employing the reductive perturbation technique, the Korteweg–de Vries equation is derived, and its nonlinear cnoidal wave (CW) solution is obtained and analyzed both analytically and numerically. …”
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Investigating soliton dynamics: Contemporary computational and numerical approaches for analytical and approximate solutions of the CDG model by Mostafa M. A. Khater, Youbing Xia, Xiao Zhang, Raghda A. M. Attia

“…This investigation employs contemporary computational and numerical techniques to derive analytical and approximate soliton solutions for the Caudrey–Dodd–Gibbon model, which represents a significant variation of the fifth-order Korteweg–de Vries equation. Diverse analytical solutions are constructed, employing distinct formats such as exponential, trigonometric, and hyperbolic functions. …”
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Head-on collision between two-counter-propagating electron acoustic soliton and double layer in an unmagnetized plasma by Shahrina Akter, M. G. Hafez

“…For nonlinear analysis of colliding wave phenomena, the coupled Korteweg–de Vries equation (KdVE), modified KdVE (mKdVE), and standard Gardner equation have been derived by adopting the extended Poincaré–Lighthill–Kuo technique. …”
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