Blow-up solutions for a case of b-family equations

Li, Zongguang; Liu, Rui

doi:10.1007/s10473-020-0402-4

Cited by 6 publications

(1 citation statement)

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“…When some parameter takes special values, obtain abundant exact kink wave solutions, singular wave solutions, periodic wave solutions, periodic singular wave solutions, and solitary wave solutions for the GMDWW equation. Through the Hamiltonian system, different phase portraits and orbits [22] are established to analyze the solitary wave solution, kink wave solution and periodic wave solution of the equation (1.1). This approach combines geometry and algebra, which can verify the solution results with graphics and improve accuracy.…”

Section: Introductionmentioning

confidence: 99%

Bifurcation of traveling wave solutions of the perturbed nonlinear Schrödinger equation

Cheng

Song

2023

Phys. Scr.

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In this paper, the traveling wave solutions of perturbed nonlinear Schr$\ddot{o}$dinger equation in nanofibers are studied by using the bifurcation theory of dynamic systems. The phase portrait and orbit analysis of perturbed nonlinear Schr$\ddot{o}$dinger equation are given in the form of graph, and the traveling wave solutions corresponding to perturbed nonlinear Schr$\ddot{o}$dinger equation under different conditions are derived and analyzed. Moreover, periodic wave solutions and periodic singular wave solutions are obtained by using Jacobian elliptic function on the basis of predecessors. And it was found that the limit of periodic wave solutions is solitary wave solutions. The limit of periodic singular wave solutions is singular wave solutions. These results provide convenience for scholars to study the physical value of this equation and allow for a deeper understanding of nonlinear phenomena and their physical essence in nanofibers.

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Section: Introductionmentioning

confidence: 99%