Abstract
In this work, a class of perturbed nonlinear Schrödinger equation is studied by using the homotopy perturbation method. Firstly, we obtain some Jacobi-like elliptic function solutions of the corresponding typical general undisturbed nonlinear Schrödinger equation through the mapping deformation method, and secondly, a homotopic mapping transform is constructed, then the approximate solution with arbitrary degree of accuracy for the perturbed equation is researched, it is pointed out that the series of approximate solution is convergent. Finally, the efficiency and accuracy of the approximate solution is also discussed by using the fixed point theorem.
Highlights
With the development of soliton theory in nonlinear science, searching for analytical exact solutions or approximate solutions of the nonlinear partial differential equations (NLPDEs) plays an important and significant role in the study of the dynamics of those nonlinear phenomena [1]
We extend the applications of HPM to solve a class of disturbed nonlinear Schrödinger equation in the nonlinear optics
We find that u 0 turns to the solution u31 in Ref.[24],and which was degenerated to the famous bright-soliton solutions u1 in Ref.[25] when m 1
Summary
With the development of soliton theory in nonlinear science, searching for analytical exact solutions or approximate solutions of the nonlinear partial differential equations (NLPDEs) plays an important and significant role in the study of the dynamics of those nonlinear phenomena [1]. Researchers had to develop some approximate methods for nonlinear theory, such as multiple-scale method [10], variational iteration method [11], indirect matching method [12] etc. The homotopy analysis method (HAM) was firstly proposed in 1992 by Liao [13], which yields a fast convergence for most of the selected problems. It showed a high accuracy and a rapid convergence to solutions of the nonlinear partial evolution equations. As a special case of HAM, He proposed the homotopy perturbation method [HPM] [16]. Based on the idea of HPM, Mo proposed the homotopic mapping method to handle some nonlinear problems with small perturbed term [17].
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