Nonlocal symmetry and explicit solutions for Drinfel’d-Sokolov-Wilson system

Ren, Bo; Liang, Zu-feng; Tang, Xiaoyan

doi:10.1140/epjp/i2016-16441-7

Cited by 27 publications

(11 citation statements)

References 28 publications

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“…Jimbo and Miwa [36] discussed the soliton equations and infinite dimensional Lie algebras. Ren et al [37] extracted non-local symmetry for DSW equation with the help of Mobius invariant form and truncated Painleve method.…”

Section: Governing Equationsmentioning

confidence: 99%

A new approach to mathematical models of Drinfeld-Sokolov-Wilson and coupled viscous Burgers’ equations in water flow

Ayata

Özkan

2021

Phys. Scr.

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In this paper, it is the first time that we implement conformable Laplace decomposition method (CLDM) to time fractional systems of Drinfeld-Sokolov-Wilson equation (DSWE) and coupled viscous Burgers’ equation (CVBE). DSWE and CVBE have an important place for cceanic, coastal sea research and they are considered as a mathematical model for shallow water waves and hydrodynmic turbulence respectively. At the end, the obtained solutions are compared with the exact solutions by the aid of tables and figures. The obtained results show that,conformable Laplace decomposition method (CLDM) is efficient, reliable, easy to apply and it gives researchers a new perspective for solving a wide variety of nonlinear fractional partial differential equations in physics.

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Section: Governing Equationsmentioning

confidence: 99%

A new approach to mathematical models of Drinfeld-Sokolov-Wilson and coupled viscous Burgers’ equations in water flow

Ayata

Özkan

2021

Phys. Scr.

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“…Compared with the local symmetry, higher-order symmetrical transformations can be built by the nonlocal symmetry [4,[19][20][21][22]. Therefore, based on the nonlocal symmetry, higher-order wave solutions and more complicated interaction solutions can be constructed by the reduction of localized symmetries or by the symmetrical transformations [5,[23][24][25][26][27][28][29][30].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal symmetries and interaction solutions for the (n + 1)-dimensional generalized Korteweg–de Vries equation

Cui

2023

Phys. Scr.

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The $(n+1)$-dimensional generalized KdV equation is presented in this paper, and we further investigate its nonlocal symmetries by different methods. It can be seen that the symmetrical transformations obtained by different nonlocal symmetries are usually equivalent. Based on the obtained Lie point symmetry as well as the $m$th finite symmetrical transformations, we obtain its soliton molecules and multiple soliton solutions. Additionally, for the case of $n=4$ various types of interaction solutions among solitons and periodic waves are obtained by the similarity reduction method.

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“…So, we can generate finite symmetry transformations by solving the initial value problem of the prolonged systems. Similarly using the truncated Painlevé approach and the Möbius (conformal) invariant form, we can drive the nonlocal symmetry for the Drinfel’d-Sokolov-Wilson equation in [ 28 ]. Meanwhile, for the use of symmetry reductions related to nonlocal symmetry, the nonlocal symmetry will be localized to the Lie point symmetry by introducing three dependent variables.…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of (1 + 1)-dimensional integro-differential Ito, KP hierarchy, CBS, MCBS and modified KdV-CBS equations

2023

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The present study computes the Lie symmetries and exact solutions of some problems modeled by nonlinear partial differential equations. The (1 + 1)-dimensional integro-differential Ito, the first integro-differential KP hierarchy, the Calogero-Bogoyavlenskii-Schiff (CBS), the modified Calogero-Bogoyavlenskii-Schiff (CBS), and the modified KdV-CBS equations are some of the problems for which we want to find new exact solutions. We employ similarity variables to reduce the number of independent variables and inverse similarity transformations to obtain exact solutions to the equations under consideration. The sine-cosine method is then utilized to determine the exact solutions.

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Nonlocal symmetry and explicit solutions for Drinfel’d-Sokolov-Wilson system

Cited by 27 publications

References 28 publications

A new approach to mathematical models of Drinfeld-Sokolov-Wilson and coupled viscous Burgers’ equations in water flow

A new approach to mathematical models of Drinfeld-Sokolov-Wilson and coupled viscous Burgers’ equations in water flow

Nonlocal symmetries and interaction solutions for the (n + 1)-dimensional generalized Korteweg–de Vries equation

Exact solutions of (1 + 1)-dimensional integro-differential Ito, KP hierarchy, CBS, MCBS and modified KdV-CBS equations

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