Abstract
Dual-mode (2+1)-dimensional Kadomtsev–Petviashvili (DMKP) equation is a new model which represents the spread of two simultaneously directional waves due to the involved term “u_{tt}(x,y,t)” in its equation. We present the construction of DMKP and search for possible solutions. The innovative tanh-expansion method and Kudryashov technique will be utilized to find the necessary constraint conditions which guarantee the existence of soliton solutions to DMKP. Supportive 3D plots will be provided to validate our findings.
Highlights
Dual-mode type is a new family of nonlinear partial differential equations which fall in the following form: [1, 2] ytt – s2yxx + ∂ – αs ∂t ∂xN(y, yx, . . .) + – βs ∂t ∂x L(ykx) = 0, (1.1)where N(y, yx, . . .) and L(ykx) : k ≥ 2 are the nonlinear and linear terms involved in the equation. y(x, t) is the unknown field-function, s > 0 is the phase velocity, |β| ≤ 1, |α| ≤ 1, β is the dispersion parameter, and α is the parameter of nonlinearity
1 Introduction Dual-mode type is a new family of nonlinear partial differential equations which fall in the following form: [1, 2]
We have studied possible solutions for dimensional Kadomtsev–Petviashvili (DMKP) and obtained the following findings:
Summary
Dual-mode type is a new family of nonlinear partial differential equations which fall in the following form: [1, 2]. With s = 0 and integrating with respect to t, the dual-mode problem is reduced to a partial differential equation of the first order in time t. [9, 10] established the dual-mode Burgers and fourth-order Burgers and obtained multiple soliton solutions by means of the simplified Hirota technique. In [11,12,13], the tanh technique and Hirota method were implemented to seek possible solutions of the two-mode coupled Burgers equation, coupled m-KdV, and coupled KdV. The dual-mode perturbed Burgers, Ostrovsky, and Schrodinger equations were established in [14, 15]
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