Hamiltonian formulation for the description of interfacial solitary waves [PDF]
Nonlinear Processes in Geophysics, 1998 We consider solitary waves propagating on the interface between two fluids, each of constant density, for the case when the upper fluid is bounded above by a rigid horizontal plane, but the lower fluid has a variable depth.
R. Grimshaw, S. R. Pudjaprasetya
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Exact Travelling-Wave Solutions of the Extended Fifth-Order Korteweg-de Vries Equation via Simple Equations Method (SEsM): The Case of Two Simple Equations. [PDF]
Entropy (Basel), 2022 Nikolova EV.
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Conservative finite volume element schemes for the complex modified Korteweg–de Vries equation
International Journal of Applied Mathematics and Computer Science, 2017 The aim of this paper is to build and validate a class of energy-preserving schemes for simulating a complex modified Korteweg–de Vries equation. The method is based on a combination of a discrete variational derivative method in time and finite volume ...
Yan Jin-Liang, Zheng Liang-Hong
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General rogue wave solutions and their dynamics in the complex modified Korteweg–de Vries equation
Results in PhysicsBy means of the Hirota bilinear method together with the Kadomtsev–Petviashvili hierarchy reduction technique, general higher-order rogue wave solutions of the complex modified Korteweg–de Vries equation are derived explicitly.
Yan Zhu +5 more
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A Jacobi Dual-Petrov Galerkin-Jacobi Collocation Method for Solving Korteweg-de Vries Equations
Abstract and Applied Analysis, 2012 The present paper is devoted to the development of a new scheme to solve the initial-boundary value Korteweg-de Vries equation which models many physical phenomena such as surface water waves in a channel.
Ali H. Bhrawy, M. M. Al-Shomrani
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Exact solutions of stochastic Burgers–Korteweg de Vries type equation with variable coefficients
Partial Differential Equations in Applied MathematicsWe will present exact solutions for three variations of the stochastic Korteweg de Vries–Burgers (KdV–Burgers) equation featuring variable coefficients.
Kolade Adjibi +6 more
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Whitham equations and phase shifts for the Korteweg-de Vries equation. [PDF]
Proc Math Phys Eng Sci, 2020 Ablowitz MJ, Cole JT, Rumanov I.
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Boundary Value ProblemsIn this paper, we consider the stochastic modified Korteweg-de Vries-Zakharov-Kuznetsov (SmKdV-ZK) equation, which is driven in the Itô sense by advection noise. We show that by solving certain deterministic counterparts of the modified Korteweg-de Vries-
Sofian T. Obeidat +2 more
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Fractal and FractionalThis paper deals with the exact wave results of the (1+1)-dimensional nonlinear compound Korteweg–De Vries and Burgers (KdVB) equation with a truncated M-fractional derivative.
Abdulrahman Alomair +2 more
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Well-posedness for some perturbations of the KdV equation with low regularity data
Electronic Journal of Differential Equations, 2008 We study some well-posedness issues of the initial value problem associated with the equation $$ u_t+u_{xxx}+eta Lu+uu_x=0, quad x in mathbb{R}, ; tgeq 0, $$ where $eta>0$, $widehat{Lu}(xi)=-Phi(xi)hat{u}(xi)$ and $Phi in mathbb{R}$ is bounded ...
Mahendra Panthee, Xavier Carvajal
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