Results 91 to 100 of about 17,995 (145)

General rogue wave solutions and their dynamics in the complex modified Korteweg–de Vries equation

Results in Physics
By 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, Lijuan Qin, Zhiqiang Yang, Zhenting Chen, Zhenyun Qin, Gui Mu   +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 Mathematics
We will present exact solutions for three variations of the stochastic Korteweg de Vries–Burgers (KdV–Burgers) equation featuring variable coefficients.
Kolade Adjibi, Allan Martinez, Miguel Mascorro, Carlos Montes, Tamer Oraby, Rita Sandoval, Erwin Suazo   +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.
europepmc   +1 more source

$ H^1 $ solutions for a modified Korteweg-de Vries-Burgers type equation

Networks and Heterogeneous Media
This paper modeled the dynamics of microbubbles coated with viscoelastic shells using the modified Korteweg-de Vries-Burgers equation, a nonlinear third-order partial differential equation.
Giuseppe Maria Coclite, Lorenzo di Ruvo
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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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Qualitative Analysis and Novel Exact Soliton Solutions to the Compound Korteweg–De Vries–Burgers Equation

Fractal and Fractional
This 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, Abdulaziz Saud Al Naim, Mustafa Bayram   +2 more
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Generation transcritical flow influenced by dissipation over a hole

Yanbu Journal of Engineering and Science
Transcritical flow of a stratified fluid over an obstacle for negative forcing amplitude (hole) that generation upstream and downstream, connected by an unsteady solution is examined.
Mohammed Daher Albalwi
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Solitary waves and shock waves for double-layered fluid flow with dispersion triplet: Zaremaoghaddam and Gear–Grimshaw models (KdV equation)

Beni-Suef University Journal of Basic and Applied Sciences
Background The Zaremaoghaddam model studies internal waves, fluid dynamics, and nonlinear wave equations. In shallow water, internal solitons, or stratified fluids, the procedure may involve modifying or applying nonlinear wave models like Korteweg–de ...
Lakhveer Kaur, Omer Mohammed Khodayer Al-Dulaimi, Farag Mahel Mohammed, Anwar Ja’afar Mohamad Jawad, Mohammad Abdelkawy, Oswaldo González-Gaxiola, Ahmed H. Arnous, Anjan Biswas   +7 more
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Ill-posedness for periodic nonlinear dispersive equations

Electronic Journal of Differential Equations, 2010
In this article, we establish new results about the ill-posedness of the Cauchy problem for the modified Korteweg-de Vries and the defocusing modified Korteweg-de Vries equations, in the periodic case. The lack of local well-posedness is in the sense
Jaime Angulo Pava, Sevdzhan Hakkaev
doaj