Abstract
The Davey-Stewartson Equation (DSE) is an equation system that reflects the evolution in finite depth of soft nonlinear packets of water waves that move in one direction but in which the waves’ amplitude is modulated in spatial directions. This paper uses the Generalized Elliptic Equation Rational Expansion (GEERE) technique to extract fresh exact solutions for the DSE. As a consequence, solutions with parameters of trigonometric, hyperbolic, and rational function are achieved. To display the physical characteristics of this model, the solutions obtained are graphically displayed. Modulation instability assessment of the outcomes acquired is also discussed and it demonstrates that all the solutions built are accurate and stable.
Highlights
Nonlinear partial differential equations (NLPDEs) are used in multiple study areas to define significant phenomena
Exact NLPDEs solutions play an important part in the research of physics, applied mathematics, and engineering, including solid state physics, fluid mechanics, population ecology, plasma physics, plasma waves, biology, optical fibres, propagation of shallow waves, heat flow, quantum mechanics, and wave propagation phenomena
The Davey-Stewartson Equation (DSE) [32] is an equation system that reflects the evolution in finite depth of soft nonlinear packets of water waves traveling in one direction but in which the amplitude of waves is modulated in spatial directions
Summary
Nonlinear partial differential equations (NLPDEs) are used in multiple study areas to define significant phenomena. The Davey-Stewartson Equation (DSE) [32] is an equation system that reflects the evolution in finite depth of soft nonlinear packets of water waves traveling in one direction but in which the amplitude of waves is modulated in spatial directions. It is of interest to derive explicit DSE equation solutions using the GEERE method. This paper is structured as follows: in Section 2 new soliton solutions are built for DSE. The DSE has the following types of soliton solutions: conventional line, algebraic, periodic, and lattice solution. To obtain fresh soliton solutions for (1) using the following traveling wave equation, we apply the widely discussed GEERE technique in [44]:. The system of algebraic equations after solving gives the following family of solutions with respect to different cases.
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