In this paper, soliton solutions to four Nonlinear Evolution Equations (NLEEs) namely Boussinesq Equation (BE), Gardner Equation (GE), (coupled) Generalized Boussinesq-Burgers Equations (GBBE) and Mikhailov-Shabat system of Equations (MSE) are obtained by the Rational Sine-Cosine Method. It has been demonstrated that the method is a convenient and effective one for solving a wide class of NLEEs encountered in various areas of Nonlinear Physical Sciences.
This paper shows the applicability of the First Integral Method in obtaining solutions of Nonlinear Partial Differential Equations (NLPDEs). The method is applied in constructing solutions of Kudryashov-Sinelshchikov equation (KSE) and Generalized Radhakrishnan-Kundu-Lakshmanan Equation (GRKLE). The First Integral Method, which is based on the Ring Theory of Commutative Algebra, is a direct algebraic method for obtaining exact solutions of NLPDEs. This method is applicable to integrable as well as nonintegrable NLPDEs. The method is an efficient method for obtaining exact solutions of many Nonlinear Evolution Equations (NLEEs).
In the present work, the First Integral Method is being applied in finding a non-soliton as well as a soliton solution of the ( 2 + 1 ) dimensional Kundu-Mukherjee-Naskar (KMN) equation which is a variant of the well-known Nonlinear Schrodinger ( NLS ) equation. Using the method, a dark optical soliton solution and a periodic trigonometric solution to the KMN equation have been suggested and the relevant conditions which guarantee the existence of such solutions are also indicated therein.
In this paper, the First Integral Method and the Sine-Cosine Method are being used in constructing optical 1-soliton solutions of Triki-Biswas Equation that plays a vital role in the study of soliton dynamics of sub-pico-second optical pulses in mono-mode optical fibers with non-Kerr law nonlinearity and subsequently some soliton and non-soliton solutions are formally obtained.
In this paper, we consider nonlinear wave equation in finite deformation elastic cylindrical rod and obtain soliton solutions by Solitary Wave Ansatz method. It is shown that the ansatz method provides a very effective and powerful mathematical tool for obtaining solutions for Nonlinear Evolution Equations (NLEEs) in nonlinear Science.
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