Bifurcations and exact soliton solutions for generalized Dullin–Gottwald–Holm equation with cubic power law nonlinearity

New Solutions for an Elliptic Equation Method and Its Applications in Nonlinear Evolution Equations

“…γ and λ are non-zero constants, we get Journal of Applied Mathematics and Physics ( ) The solutions (3.46)-(3.50) have not been obtained in [33], they are new ones.…”

“…We consider generalized Dullin-Gottwald-Holm equation [30] In [33], the authors studied the bifurcation of Equation (3.32) and obtained some travelling wave solutions by the modified simplest equation method. To our knowledge, there is no study on the exact solutions for Equation (3.32) other than [33]. Using (2.1)-(2.5), we will get some new traveling wave solutions to Equation (3.32).…”

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

“…, k k -parameter plane, as shown in Figure 1. Using the bifurcation theory of differential equation [35] [36] [37] [38], we obtain the phase portraits of system (2.5), as shown in Figure 2.…”

“…Obviously, there is no single way to solve the soliton solutions of all nonlinear evolution equations, which leads to the generation of many new methods, such as the 2 ′ G G -expansion method and the sine-cosine method [20], the functional variable method and first integral approach [21], the semi-inverse variational principle [22], Lie symmetry approach [23], the method of F-expansion [24] [25], the modified simple equation method and the trial equation method [26] [27], the asymmetric method [28], the Gaussian ansatz [29] [30], the soliton perturbation theory [31] [32], the simplest equation method and the ′ G G -expansion method [33] [34], the theory of dynamical systems [35] [36] [37] [38].…”

Soliton Solutions of the Generalized Dullin-Gottwald-Holm Equation with Parabolic Law Nonlinearity

“…Besides, 𝛾 and 𝜎 are coefficients of the parabolic law nonlinearity form that occurs in optical fibers. Yang et al (2022) studied exact soliton solutions of the gDGH equation with cubic power law nonlinearity. They also investigated the bifurcations of the solutions.…”