Multiple Soliton Solutions Of (2+1)-Dimensional Potential Kadomtsev-Petviashvili Equation (original) (raw)
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Physica Scripta, 2012
We give an introduction to a new direct computational method for constructing multiple soliton solutions to nonlinear equations with variable coefficients in the Kadomtsev-Petviashvili (KP) hierarchy. We discuss in detail how this works for a generalized (3 + 1)-dimensional KP equation with variable coefficients. Explicit soliton, multiple soliton and singular multiple soliton solutions of the equation are obtained under certain constraints on the coefficient functions. Furthermore, the characteristic-line method is applied to discuss the solitonic propagation and collision under the effect of variable coefficients.
Filomat
The Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) model equations as a water wave model, are governing equations, for fluid flows, describes bidirectional propagating water wave surface. The soliton solutions for (2+1) and (3+1)-Dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equations have been extracted. The solitary wave ansatz method are adopted to approximate the solutions. The corresponding integrability criteria, also known as constraint conditions, naturally emerge from the analysis of the problem.
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Romanian Reports in Physics, 2013
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International Journal of Physical Sciences, 2013
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Applied Mathematics and Computation, 2001
In this paper, we present a computational approach to develop soliton solutions of the nonlinear Kadomtsev±Petviashvili equation. Our approach rests mainly on the Adomian decomposition method to include few components of the decomposition series. The proposed framework is presented in a general way so that it can be used in nonlinear evolution equations of the same type. Numerical examples are tested to illustrate the proposed scheme. Ó