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Karpman, V. and Maslov, E. (1977) Perturbation Theory for Solitons. Journal of Experimental and Theoretical Physics, 73, 537-559.

has been cited by the following article:

• TITLE: Solitons and Bifurcations for the Generalized Tzitzéica Type Equation in Nonlinear Fiber Optics

  AUTHORS: Xujie Jiang

  KEYWORDS: Generalized Tzitzéica Type Equation, Homoclinic Orbit, Periodic Wave Solution, Bright Soliton, Dark Soliton

  JOURNAL NAME: Journal of Applied Mathematics and Physics, Vol.11 No.10, October 30, 2023

  ABSTRACT: Solitons and bifurcations for the generalized Tzitzéica type equation are studied by using the theory of dynamical systems and Hamilton function. With the help of Maple and bifurcation theory of differential equations, the bifurcation parameter conditions and all the bifurcation phase portraits are obtained. Because the same energy value of the Hamiltonian function is corresponding to the same orbit, thus the periodic wave solutions, bright soliton and dark soliton solutions are defined.