A New Approach of Bernoulli Sub-ODE Method to Solve Nonlinear PDEs

In this paper, a new approach of the Bernoulli Sub-ODE method is proposed and this method is applied to solve the modified Liouville equation and the regularized long wave equation. As a result some new traveling wave solutions for them are successfully established. When the parameters are taken as special values, the solitary wave solutions are originated from these traveling wave solutions. Further, graphical representation of some solutions are given to visualize the dynamics of the equation. The results reveal that this method may be useful for solving higher order nonlinear partial differential equations

A Riccati-Bernoulli Sub-ODE Method for the Resonant Nonlinear Schrödinger Equation with Both Spatio-Temporal Dispersions and Inter-Modal

This work uses the Riccati-Bernoulli sub-ODE method in constructing various new optical soliton solutionsto the resonant nonlinear Schrodinger equation with both Spatio-temporal dispersion and inter-modal dispersion. Actually, the proposed method is effective tool to solve many other nonlinear partial differential equations in mathematical physics. Moreover this method can give a new infinite sequence of solutions. These solutions are expressed by hyperbolic functions, trigonometric functions and rational functions. Finally, with the aid of Matlab release 15, some graphical simulations were designed to see the behavior of these solutions

Application of Bernoulli Sub-ODE Method For Finding Travelling Wave Solutions of Schrodinger Equation Power Law Nonlinearity

In this paper, the exact travelling wave solution of the Schr¨odinger equation with power law nonlinearity is studied by the Sub-ODE method. It is shown that the method is one of the most effective approaches for finding exact solutions of nonlinear differential equations

Existence theories and exact solutions of nonlinear PDEs dominated by singularities and time noise

The current research deals with the exact solutions of the nonlinear partial differential equations having two important difficulties, that is, the coefficient singularities and the stochastic function (white noise). There are four major contributions to contemporary research. One is the mathematical analysis where the explicit a priori estimates for the existence of solutions are constructed by Schauder’s fixed point theorem. Secondly, the control of the solution behavior subject to the singular parameter ϵ when ϵ → 0. Thirdly, the impact of noise that is present in the differential equation has been successfully handled in exact solutions. The final contribution is to simulate the exact solutions and explain the plots

SOLITARY WAVE SOLUTIONS FOR THE (2+1) CBS EQUATION

The aim of this paper is to investigate the traveling wave solution of the Calogero-Bogoyavlenskii-Schiff (CBS) equation using the Riccati-Bernoulli (RB) sub-ODE method. The (RB) sub-ODE method is used to secure traveling wave solutions that are expressed explicitly and graphically in 3D. The RB sub-ODE technique is a powerful tool that is used to solve various nonlinear partial differential equations (NPDEs). The obtained soliton solutions have been demonstrated by relevant figures

OPTICAL SOLITON SOLUTIONS FOR THE NONLINEAR THIRD-ORDER PARTIAL DIFFERENTIAL EQUATION

In this paper, the Riccati-Bernoulli (RB) sub-ODE method is used to find the solitary wave solutions for a third-order nonlinear partial differential equation (NLPDE). The traveling wave transformation along with RB sub-ODE equation is used to convert the third-order NLPDE to the set of algebraic equations. Solving the set of algebraic equations generates the analytical solution of the third-order NLPDE. The RB sub-ODE method is a powerful and simple mathematical tool for solving complex NLPDE. The solitary wave solutions obtained play a vital role in mathematical physics

Functional variable method to the Chiral nonlinear Schrodinger equation

In this paper, we study the different types of new soliton solutions to the Chiral nonlinear Schrodinger equation with the aid of the functional variable method. Then, we get some special soliton solutions for Chiral nonlinear Schrodinger equation. The parameters of the soliton envelope are obtained as a function of the dependent model coefficients.Publisher's Versio