Soliton solutions to resonant nonlinear schrodinger's equation with time-dependent coefficients by modified simple equation method

Abstract

This paper studies resonant nonlinear Schrodinger's equation with time-dependent coefficients and four forms of nonlinear media. They are Kerr law, power law, parabolic law and dual-power law. Soliton solutions are recovered by the aid of modified simple equation method.

Exact solutions of (1 + 1)-dimensional integro-differential Ito, KP hierarchy, CBS, MCBS and modified KdV-CBS equations

“…The most important problem in real-world phenomena is computing exact solutions of nonlinear PDEs. The homogeneous balance method [ 1 ], the Darboux transform method [ 2 , 3 ], the first integral method [ 4 , 5 ], the tanh function method [ 6 ], the modified simple equation method [ 7 , 8 ], the method of the auxiliary equation [ 9 , 10 ], the ( G ′/ G )-expansion method [ 11 , 12 ], the F-expansion method [ 13 , 14 ], Jacobi elliptic function method [ 15 , 16 ], and Lie symmetry method [ 17 – 19 ] are some of the important methods available to compute exact solutions of nonlinear PDEs. Although there is no universal strategy for solving nonlinear PDEs, Lie symmetry analysis is one of the most effective and reliable techniques for discovering new exact solutions to nonlinear PDEs arising in applied mathematics and physics.…”

Resonant Optical Solitons in (3 + 1)-Dimensions Dominated by Kerr Law and Parabolic Law Nonlinearities

“…Several integration schemes have been implemented to examine the behavior of solitons such as ansatz method, semiinverse variational principle, simplest equation approach, first integral method, functional variable method, sine-cosine function method, (G 0 =G)-expansion method, trial solution approach, generalized extended tanh method, modified simple equation method, and improved extended tanh-equation method. For more details, readers are referred to references [14][15][16][17][18][19][20][21][22][23][24][25].…”

Different Physical Structures of Solutions for a Generalized Resonant Dispersive Nonlinear Schrödinger Equation with Power Law Nonlinearity

“…Recently, the GRD-NLSE has been studied by many authors to examine the behaviour of solutions. Several integration schemes have been implemented to construct exact solutions such as ansatz method [13,14], semi-inverse variational principle [15], simplest equation approach [16], first integral method [17], functional variable method, sine-cosine function method [18], ( / )-expansion method [19], trial solution approach [20], generalised extended tanh method [21], modified simple equation method [22], and improved extended tanh-equation method [23].…”