Variable Separation Approach to Solve (2+1)-Dimensional Generalized Burgers System: Solitary Wave and Jacobi Periodic Wave Excitations

Zheng, Chunxiong

doi:10.1088/0253-6102/41/3/391

Cited by 6 publications

(1 citation statement)

References 10 publications

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“…Osman et al also used the Lie group method to reduce the (2 +1)-dimensional CBEs to get the non-travelling wave solutions. In reference [19], Zheng et al obtained general separations of variable solutions of CBEs with the standard truncated Painlevé expansion and separation of variables method. Meanwhile, Zheng et al obtained new types of Jacobi periodic wave solutions and excitationscompacton by introducing suitable low-dimensional segmented smooth functions and Jacobi elliptic functions.…”

Section: Introductionmentioning

confidence: 99%

The Lie symmetry analysis, optimal system and exact solutions of the (2+1)-dimensional variable coefficients integrable coupled Burgers equations

Jin,

Yang,

Xin

2023

Phys. Scr.

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The variable coefficients integrable coupled Burgers equations (vcICBs) are researched by the Lie symmetry analysis method. The infinitesimal generators, commutative relations and adjoint relations are given. Optimal system of vcICBs are studied by Olver’s method. Based on the optimal system, the (2+1)-dimensional vcICB equations are reduced to (1+1)-dimensional equations. Some new exact solutions of vcICB equations are derived. Some kink solutions, breathe wave solutions and soliton solutions are got by utilising (G' /G)-expansion method, Riccati equation method, Tanh-expansion method and Painlevé analysis method. By altering different coefficient functions, many different types of exact solutions can be derived. The effect of the coefficient functions on the solution is analysed. By studying the evolution of the solution with time t, the dynamic behaviors of the solutions are analysed.

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Section: Introductionmentioning

confidence: 99%

The Lie symmetry analysis, optimal system and exact solutions of the (2+1)-dimensional variable coefficients integrable coupled Burgers equations

Jin,

Yang,

Xin

2023

Phys. Scr.

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Instruction on the construction of coherent structures based on variable separation solutions of (2+1)-dimensional nonlinear evolution equations in fluid mechanics

Jiang

2019

Nonlinear Dyn

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Novel variable separation solutions and exotic localized excitations via the ETM in nonlinear soliton systems

Dai

Zhang

2006

Journal of Mathematical Physics

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In this paper, first, the ETM is applied to obtain variable separation solutions of (2+1)-dimensional systems. A common formula with some arbitrary functions is derived to describe suitable physical quantities for some (2+1)-dimensional models such as the generalized Nizhnik-Novikov-Veselov, Davey-Stewartson, Broer-Kaup-Kupershmidt, Boiti-Leon-Pempinelli, integrable Kortweg-de Vries (KdV), breaking soliton and Burgers models. The universal formula in Tang, Lou, and Zhang [Phys. Rev. E 66, 046601 (2002)] can be simplified to the common formula in the present paper, which indicates that redundant process is included there since the easier variable separation form can be employed without loss of generality. Second, this method is successfully generalized to (1+1)-dimensional systems, such as coupled integrable dispersionless, long-wave–short-wave resonance interaction and negative KdV models, and obtain another common formula to describe suitable physical fields or potentials of these (1+1)-dimensional models, which is similar to the one in (2+1)-dimensional systems. Moreover, it also is extended to (3+1)-dimensional Burgers system, and find that the common formula in (2+1)-dimensional systems is also appropriate to describe the (3+1)-dimensional Burgers system. The only differences are that the function q is a solution of a constraint equation and p is an arbitrary function of three independent variables. Finally, based on the common formula for (2+1)-dimensional systems and by selecting appropriate multivalued functions, interactions among special dromion, special peakon and foldon are investigated. The interactions between two special dromions, and between two special peakons, both possess novel properties, that is, there exist a multivalued foldon in the process of their collision, which is different from the reported cases in previous literature. Furthermore, the explicit phase shifts for all the local excitations offered by the common formula have been given, and are applied to these novel interactions in detail.

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Variable Separation Approach to Solve (2+1)-Dimensional Generalized Burgers System: Solitary Wave and Jacobi Periodic Wave Excitations

Cited by 6 publications

References 10 publications

The Lie symmetry analysis, optimal system and exact solutions of the (2+1)-dimensional variable coefficients integrable coupled Burgers equations

The Lie symmetry analysis, optimal system and exact solutions of the (2+1)-dimensional variable coefficients integrable coupled Burgers equations

Instruction on the construction of coherent structures based on variable separation solutions of (2+1)-dimensional nonlinear evolution equations in fluid mechanics

Novel variable separation solutions and exotic localized excitations via the ETM in nonlinear soliton systems

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