Hosseini K., Matinfar M., Mirzazadeh M.
Soliton Solutions of High-order Nonlinear Schrödinger Equations with Different Laws of Nonlinearities
2021, vol. 26, no. 1, pp. 105-112
In the present paper, high-order nonlinear Schrödinger equations in non-Kerr law media with different laws of nonlinearities are studied. In this respect, after considering a complex envelope and distinguishing the real and imaginary portions of the models, describing the propagation of solitons through nonlinear optical fibers, their soliton solutions are obtained using the well-organized new Kudryashov method. It is believed that the new Kudryashov method provides an effective mathematical tool to look for soliton solutions of high-order nonlinear Schrödinger equations.
Hosseini K., Samavat M., Mirzazadeh M., Ma W., Hammouch Z.
A New $(3+1)$-dimensional Hirota Bilinear Equation: Its Bäcklund Transformation and Rational-type Solutions
2020, vol. 25, no. 4, pp. 383-391
The behavior of specific dispersive waves in a new $(3+1)$-dimensional Hirota bilinear (3D-HB) equation is studied. A Bäcklund transformation and a Hirota bilinear form of the model are first extracted from the truncated Painlevé expansion. Through a series of mathematical analyses, it is then revealed that the new 3D-HB equation possesses a series of rational-type solutions. The interaction of lump-type and 1-soliton solutions is studied and some interesting and useful results are presented.