New Exact Solutions and Modulation Instability for the Nonlinear (2+1)-Dimensional Davey-Stewartson System of Equation

Boateng, Kwasi; Yang, Weiguo; Apeanti, Wilson Osafo; Yaro, David

doi:10.1155/2019/3879259

Cited by 5 publications

(3 citation statements)

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“…So, studying numerous other equations with more different features and forms is critical in order to develop many more physical qualities and features. Inspired by this, we study with the application of the enhanced modified extended tanh expansion method (eMETEM) [38] to the (2 + 1)-DSE [39] and the (2 + 1)-CCMS [40].…”

Section: Introductionmentioning

confidence: 99%

“…The (2 + 1)-DSE equation has been the subject of some studies before. Such as, variablecoefficient form in [43], by using the extended exponential function and the Khater II methods [44], new exact solutions and modulation instability via generalized elliptic equation rational expansion [39], soliton solutions of the generalized DSE with the complex coefficients by using extended tanh-coth and modified simple equation method [45], new extended generalized Kudryashov method is applied in [46], Bäcklund transformation and Lax pair [47], the mapping method [48].…”

Section: Introductionmentioning

confidence: 99%

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On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Ozisik,

Esen,

Secer

et al. 2024

Preprint

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In this work, we take into account the (2 + 1)-Davey Stewartson equation (DSE) and (2 + 1)-Complex Coupled Maccari System (CCMS) and their analytical solutions. Besides, we tackle with the role of the problem parameters on the soliton behavior which the investigated DSE produces. Exact traveling wave solutions are highly useful in numerical and analytical theories in such equations. We use an efficient analytical approach to calculate the soliton solutions of these models. We have shown that soliton solutions’ features can represent the spread of propagation on the wave fronts and show a reasonable dependency on parameter values. Some of the solutions discovered in three and two-dimensional arrangements can also be described in graphic representations for their behavior. The results show that the technique is easy applicable, efficient, reliable, robust and categorical when it comes to find exact solutions for different nonlinear models. Moreover, the problem parameters and the coupling coefficients have significant effects on the behavior of the solitons of the DSE and this examination is studied for the first time in this article.

show abstract

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Ozisik,

Esen,

Secer

et al. 2024

Preprint

View full text Add to dashboard Cite

show abstract

“…where u � u(t, x, y) is the complex wave envelope, v � v(t, x, y) is the real forcing function, a 1 (t) and a 2 (t) are real functions with respect to time t, which stand for group velocity dispersion terms, b 1 (t) and b 2 (t) represent the quadratic nonlinearity and cubic nonlinear coefficient term, respectively, and s 1 and s 2 are constants. When the coefficients in equation ( 1) are constant, equation ( 1) is called the Davey-Stewartson system [11][12][13][14][15]. It is a very important nonlinear Schrödinger equation, which is usually used to describe the nonlinear wave packet of finite depth.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation Analysis and Single Traveling Wave Solutions of the Variable‐Coefficient Davey–Stewartson System

Han

Wen

2022

Discrete Dynamics in Nature and Society

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This paper mainly studies the bifurcation and single traveling wave solutions of the variable-coefficient Davey–Stewartson system. By employing the traveling wave transformation, the variable-coefficient Davey–Stewartson system is reduced to two-dimensional nonlinear ordinary differential equations. On the one hand, we use the bifurcation theory of planar dynamical systems to draw the phase diagram of the variable-coefficient Davey–Stewartson system. On the other hand, we use the polynomial complete discriminant method to obtain the exact traveling wave solution of the variable-coefficient Davey–Stewartson system.

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On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Ozisik,

Esen,

Secer

et al. 2024

Opt Quant Electron

View full text Add to dashboard Cite

In this work, we take into account the (2+1)-Davey Stewartson equation (DSE) and the (2+1)-complex coupled Maccari system (CCMS) and their analytical solutions. Besides, we tackle the role of the problem parameters on the soliton behavior produced by the presented DSE. Exact traveling wave solutions are highly useful in numerical and analytical theories for such equations. While numerical methods are widely used, improving analytical approaches for obtaining analytical solutions is necessary for a deeper understanding of dynamics. This study marks a significant milestone by implementing the efficient analytical approach, enhanced modified extended tanh expansion method, for the first time to the (2+1)-DSE and (2+1)-CCMS equations, thereby making a notable contribution to the existing literature. We have shown that features of the soliton solutions can represent the spread of propagation on the wavefronts and show a reasonable dependency on parameter values. Some of the solutions discovered in three- and two-dimensional arrangements can also be described in graphic representations of their behavior. With the help of the graphical depictions, bright, singular, and periodic singular soliton characters for the $$(2+1)$$ ( 2 + 1 ) -DSE and singular, dark, bright, and periodic singular soliton characters for the $$(2+1)$$ ( 2 + 1 ) -CCMS are acquired. The results show that the utilized analytical technique is easily applicable, efficient, reliable, robust, and categorical when it comes to finding analytical solutions for different nonlinear models. Moreover, the problem parameters and the coupling coefficients have significant influences on the behavior of the solitons of the DSE, and this examination is studied for the first time in this article.

show abstract

New Exact Solutions and Modulation Instability for the Nonlinear (2+1)-Dimensional Davey-Stewartson System of Equation

Cited by 5 publications

References 50 publications

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

Bifurcation Analysis and Single Traveling Wave Solutions of the Variable‐Coefficient Davey–Stewartson System

On the soliton solutions to some system of complex coupled nonlinear models and the effect of the coupling coefficients

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