Trapped Solitary Waves in a Periodic External Force: A Numerical Investigation Using the Whitham Equation and the Sponge Layer Method by Marcelo V. Flamarion, Roberto Ribeiro-Jr, Diogo L. S. S. Vianna, Alex M. Sato

“…In addition, we compare the results predicted by the Whitham equation with those of the Korteweg–de Vries equation.…”
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Symmetry reductions and conservation laws of a modified-mixed KdV equation: exploring new interaction solutions by Nauman Raza, Maria Luz Gandarias, Ghada Ali Basendwah

“…This article represented the investigation of the modified mixed Korteweg-de Vries equation using different versatile approaches. …”
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Regional eigenmodes of global spectral dynamics. Part I: Theoretical background by Frank Schmidt, Wei Li, Antal Snubrskije

“…This is illustrated here for analysis of a 1-dimensional Burgers/Korteweg-DeVries equation. Application to a shallow water lower troposphere will be given in Part II.…”
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Fractional view analysis of Kersten-Krasil'shchik coupled KdV-mKdV systems with non-singular kernel derivatives by M. Mossa Al-Sawalha, Rasool Shah, Adnan Khan, Osama Y. Ababneh, Thongchai Botmart

“…The approximate solution of the Kersten-Krasil'shchik coupled Korteweg-de Vries-modified Korteweg-de Vries system is obtained in this study by employing a natural decomposition method in association with the newly established Atangana-Baleanu derivative and Caputo-Fabrizio derivative of fractional order. The Korteweg-de Vries equation is considered a classical super-extension in this system. …”
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Exploring solitary wave solutions to the simplified modified camassa-holm equation through a couple sophisticated analytical approaches by Sujoy Devnath, Shahansha Khan, M. Ali Akbar

“…The simplified modified Camassa-Holm equation, a developed Korteweg-de Vries equation, is an integrable nonlinear dispersive water wave equation with potential applications in diverse fields such as shallow water waves, liquid drop patterning, water surface waves in channels, tsunamis in coastal regions, ocean engineering, etc. …”
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Shallow Water Waves and Conservation Laws with Dispersion Triplet by Anjan Biswas, Nyah Coleman, Abdul H. Kara, Salam Khan, Luminita Moraru, Simona Moldovanu, Catalina Iticescu, Yakup Yıldırım

“…This paper secures solitary waves and conservation laws to the familiar Korteweg–de Vries equation and Gardner’s equation with three dispersion sources. …”
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The analysis of the fractional-order system of third-order KdV equation within different operators by Noufe H. Aljahdaly, Rasool Shah, Ravi P. Agarwal, Thongchai Botmart

“…This paper studies the fractional system of the third-order Korteweg-De Vries equation under the fractional derivatives of Caputo, Atangana-Baleanu and Yang-Srivastava-Machado. …”
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Registration of the atmospheric effect of the Hunga Tonga volcano eruption by Sorokin A. G., Dobrynin V. A.

“…Using the solution of the linearized Korteweg — de Vries equation, we estimate the energy released during the volcanic eruption. …”
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Solitary wave solution of (3+1)-dimensional cylindrical Kadomstev–Petviashvili equation in warm opposite polarity dusty plasma by S. Tarofder, A. Mannan, A.A. Mamun

“…The standard reductive perturbation method is employed to derive the (3+1)-dimensional cylindrical Kadomstev–Petviashvili (KP) equation (also known as cylindrical Korteweg–de Vries equation), which admits solitary wave solution for small but finite amplitudes. …”
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An Effect of Electrokinetics Phenomena on Nonlinear Wave Propagation in Bubbly Liquids by G. Panahov, E. Abbasov, S. Bakhtiyarov, P. Museibli

“…Numerical simulations have been conducted to study the nonlinear waves described by the nonlinear Burgers-Korteweg-de Vries equation. The numerical simulations showed that the electrokinetic processes significantly affect the wave propagation process. …”
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Spatial Analyticity of Solutions to Korteweg–de Vries Type Equations by Keltoum Bouhali, Abdelkader Moumen, Khadiga W. Tajer, Khdija O. Taha, Yousif Altayeb

“…The Korteweg–de Vries equation (KdV) is a mathematical model of waves on shallow water surfaces. …”
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Exploring the wave solutions of a nonlinear non-local fractional model for ocean waves by Chen Yue, Miao Peng, M. Higazy, Mostafa M. A. Khater

“…Various analytical solutions, such as exponential, trigonometric, and hyperbolic, have been formulated differently for this model, which is a specific derivation of the well-known Korteweg–de Vries equation. Density charts in two and three dimensions are used to visualize the behavior of a single soliton in reality through simulations. …”
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Kinetic Alfvén solitary waves in a low-β plasma with regularized kappa-distributed electrons by Wedad Albalawi, Muhammad Khalid, C. G. L. Tiofack, S. A. El-Tantawy

“…We then use the Korteweg–de Vries equation to investigate the KAWs in this model, which we obtained from the reductive perturbation method. …”
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The long-time behavior of solitary waves for the weakly damped KdV equation by Yansheng Zhong, Riguang Wu

“…Abstract In this paper, we first introduce the long-time behavior stability of solitary waves for the weakly damped Korteweg–de Vries equation. More concretely, solutions of the dissipative system with the initial values near a c 0 $c_{0}$ -speed solitary wave, are approximated by a long curve on the family of solitary waves with the time-varying speed | c ( t ) − c 0 | $|c(t)-c_{0}|$ being small, in the long-time period (i.e., 0 ⩽ t ⩽ O ( 1 ϵ τ ) $0\leqslant t\leqslant O(\frac{1}{\epsilon ^{\tau}})$ ). …”
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On the Method of Transformations: Obtaining Solutions of Nonlinear Differential Equations by Means of the Solutions of Simpler Linear or Nonlinear Differential Equations by Nikolay K. Vitanov

“…As an example of this, we use the Korteweg–de Vries equation and its solutions. Traveling wave solutions of nonlinear differential equations are of special interest in this article. …”
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Diversity of wave structures to the conformable fractional dynamical model by U. Younas, J. Ren

“…The governing equation is stretch for the Korteweg-de-Vries equation that represents the unidirectional propagation of small amplitude long waves on the surface of hydro magnetic and acoustic waves in a channel, especially for shallow water. …”
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On the Propagation Model of Two-Component Nonlinear Optical Waves by Aleksandr O. Smirnov, Eugeni A. Frolov

“…Also, knowledge of the monodromy matrix allows us to find stationary equations that are analogs of the Novikov equations for the Korteweg–de Vries equation. In addition, the characteristic equation of the monodromy matrix corresponds to the spectral curve equation of the relevant multiphase solution for the integrable nonlinear equation. …”
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Soliton Decomposition of the Box-Ball System by Pablo A. Ferrari, Chi Nguyen, Leonardo T. Rolla, Minmin Wang

“…The box-ball system (BBS) was introduced by Takahashi and Satsuma as a discrete counterpart of the Korteweg-de Vries equation. Both systems exhibit solitons whose shape and speed are conserved after collision with other solitons. …”
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Solitons in lattice field theories via tight-binding supersymmetry by Balasubramanian, Shankar, Patoary, Abu, Galitski, Victor

“…Abstract Reflectionless potentials play an important role in constructing exact solutions to classical dynamical systems (such as the Korteweg-de Vries equation), non-perturbative solutions of various large-N field theories (such as the Gross-Neveu model), and closely related solitonic solutions to the Bogoliubov-de Gennes equations in the theory of superconductivity. …”
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Fluid flow through vegetation by Wong, CYH

“…For shallow-water waves, we explore how cnoidal waves, nonlinear periodic solutions of the Korteweg-de Vries equation, evolve on horizontal substrates. …”