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Numerical algorithm based on an implicit fully discrete local discontinuous Galerkin method for the time-fractional KdV-Burgers-Kuramoto equation
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In this paper, an implicit fully discrete local discontinuous Galerkin (LDG) finite element method is considered for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation.Abstract:
In this paper, an implicit fully discrete local discontinuous Galerkin (LDG) finite element method is considered for solving the time-fractional KdV-Burgers-Kuramoto (KBK) equation. The scheme is based on a finite difference method in time and local discontinuous Galerkin methods in space. We prove that our scheme is unconditional stable and L2 error estimate for the linear case with the convergence rate O(hk+1 + (Delta t)2+ (Delta t)alpha/2hk+1/2). Numerical examples are presented to show the efficiency and accuracy of our scheme.read more
Citations
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New extended Kadomtsev–Petviashvili equation: multiple soliton solutions, breather, lump and interaction solutions
TL;DR: In this article, a new extended Kadomtsev-Petviashvili (eKP) equation was developed and the Painleve analysis was used to confirm the integrability of the eKP equation.
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A new (3+1)-dimensional Kadomtsev–Petviashvili equation and its integrability, multiple-solitons, breathers and lump waves
TL;DR: A new (3+1)-dimensional integrable Kadomtsev–Petviashvili equation is developed and its integrability is verified by the Painleve analysis, and the abundant dynamical behaviors for these solutions are discovered.
Journal ArticleDOI
Kadomtsev–Petviashvili hierarchy: N-soliton solutions and distinct dispersion relations
TL;DR: This paper uses the simplified Hirota’s method to study two integrable members of this new KP hierarchy and shows that these two equations give multiple soliton solutions that possess the same amplitude and the same phase shift, but with distinct dispersion relations.
Journal ArticleDOI
Direct meshless local Petrov–Galerkin (DMLPG) method for time-fractional fourth-order reaction–diffusion problem on complex domains
Mostafa Abbaszadeh,Mehdi Dehghan +1 more
TL;DR: A new numerical scheme based on the fast and efficient meshless local weak form DMLPG method for solving the fractional fourth-order partial differential equation on computational domains with complex shape is developed.
Journal ArticleDOI
Kadomtsev–Petviashvili hierarchy: two integrable equations with time-dependent coefficients
Abdul-Majid Wazwaz,Gui-Qiong Xu +1 more
TL;DR: In this article, the authors investigated two members of the Kadomtsev-Petviashvili (KP) hierarchy with time-dependent coefficients and used the simplified Hirota method to derive multiple soliton solutions for each equation.
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