Bifurcations and new exact travelling wave solutions for the Gerdjikov-Ivanov equation. (English) Zbl 1222.35184
Summary: The Gerdjikov–Ivanov equation is investigated by using the bifurcation theory and the method of phase portraits analysis. The existence of every kind of travelling waves is proved, in some conditions, exact parametric representations of above travelling waves in explicit form are obtained.
MSC:
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 35B32 | Bifurcations in context of PDEs |
| 35C07 | Traveling wave solutions |
| 37G15 | Bifurcations of limit cycles and periodic orbits in dynamical systems |
Keywords:
Gerdjikov; Ivanov equation; homoclinic orbit; heteroclinic orbit; travelling wave; exact solutionReferences:
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