Standing Wave Solutions for the Discrete Coupled Nonlinear Schrödinger Equations with Unbounded Potentials

We demonstrate the existence of standing wave solutions of the discrete coupled nonlinear Schrödinger equations with unbounded potentials by using the Nehari manifold approach and the compact embedding theorem. Sufficient conditions are established to show that the standing wave solutions have both of the components not identically zero.

Download Full-text

Stability and response of trapped solitary wave solutions of coupled nonlinear Schrödinger equations in an external, $\mathcal{PT}$- and supersymmetric potential

Journal of Physics A Mathematical and Theoretical ◽

10.1088/1751-8121/abb278 ◽

2020 ◽

Vol 53 (45) ◽

pp. 455702

Author(s):

Efstathios G Charalampidis ◽

John F Dawson ◽

Fred Cooper ◽

Avinash Khare ◽

Avadh Saxena

Keyword(s):

Solitary Wave ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Solitary Wave Solutions ◽

Coupled Nonlinear Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Wave Solutions ◽

Nonlinear Schrodinger Equations ◽

Coupled Nonlinear Schrodinger Equations

Download Full-text

Approximate interacting solitary wave solutions for a pair of coupled nonlinear Schrödinger equations

Physical Review E ◽

10.1103/physreve.49.5731 ◽

1994 ◽

Vol 49 (6) ◽

pp. 5731-5741 ◽

Cited By ~ 13

Author(s):

J. C. Bhakta

Keyword(s):

Solitary Wave ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Solitary Wave Solutions ◽

Coupled Nonlinear Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Wave Solutions ◽

Nonlinear Schrodinger Equations ◽

Coupled Nonlinear Schrodinger Equations

Download Full-text

Dynamical Behavior and the Classification of Single Traveling Wave Solutions for the Coupled Nonlinear Schrödinger Equations with Variable Coefficients

Advances in Mathematical Physics ◽

10.1155/2021/9955023 ◽

2021 ◽

Vol 2021 ◽

pp. 1-10

Author(s):

Zhao Li ◽

Peng Li ◽

Tianyong Han

Keyword(s):

Traveling Wave ◽

Variable Coefficients ◽

Nonlinear Schrödinger Equations ◽

Schrodinger Equations ◽

Schrödinger Equations ◽

Coupled Nonlinear Schrödinger Equations ◽

Nonlinear Schrödinger ◽

Wave Solutions ◽

Nonlinear Schrodinger Equations ◽

Coupled Nonlinear Schrodinger Equations

In this paper, the dynamical properties and the classification of single traveling wave solutions of the coupled nonlinear Schrödinger equations with variable coefficients are investigated by utilizing the bifurcation theory and the complete discrimination system method. Firstly, coupled nonlinear Schrödinger equations with variable coefficients are transformed into coupled nonlinear ordinary differential equations by the traveling wave transformations. Then, phase portraits of coupled nonlinear Schrödinger equations with variable coefficients are plotted by selecting the suitable parameters. Furthermore, the traveling wave solutions of coupled nonlinear Schrödinger equations with variable coefficients which correspond to phase orbits are easily obtained by applying the method of planar dynamical systems, which can help us to further understand the propagation of the coupled nonlinear Schrödinger equations with variable coefficients in nonlinear optics. Finally, the periodic wave solutions, implicit analytical solutions, hyperbolic function solutions, and Jacobian elliptic function solutions of the coupled nonlinear Schrödinger equations with variable coefficients are constructed.

Download Full-text