Dynamic behavior of solitons solutions of some nonlinear models.
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Date
2022-05-26
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UMT Lahore
Abstract
In this dissertation, several analytical solutions of some important models of nonlinear partial differential equations are presented. Certain novel optical solitons solutions including dark, singular, periodic singular and bright-singular combo optical solitons solutions of highly dispersive nonlinear Schrödinger equation with cubic law and cubic-quintic-septic law nonlinearities are constructed by using the Kudryashov’s method and generalized tanh method. The obtained solutions are interpreted by plotting some graphs.
Further, the exact solutions of Kudryashov-Sinelshchikov equation, which is the generalization of the Korteweg-De Vries equation are constructed and the non-linear waves in mixtures of gas-liquid in the absence of viscosity are described by utilizing the Sardar-subequation method and the new extended hyperbolic function method. For more illustration of our retrieved solutions, some distinct kinds of 2D and 3D graphs are presented.
Next, the extended direct algebraic method is applied to examine the dark, singular, combined dark-bright, combined bright-singular and periodic singular solitons as well as hyperbolic and trigonometric functions solutions of well known nonlinear model Biswas-Arshad equation without four-wave mixing terms in birefringent fibers in the form of two vector polarity components. Moreover, the novel exact and soliton solutions are extracted in the form of generalized trigonometric and hyperbolic functions solutions of Newel-Whitehead-Segel equation and Zeldovich equation via the new extended direct algebraic method by taking the special values to involved parameters in the method. At the end, the obtained solutions are interpreted physically by plotting two and three-dimensional graphs using the softwares Maple and Mathematica.