Rogue Wave Solutions and Generalized Darboux Transformation for an Inhomogeneous Fifth-Order Nonlinear Schrödinger Equation

Song, Ni; Zhang, W.; Wang, Peng; Xue, Yong

doi:10.1155/2017/6910926

Cited by 4 publications

(1 citation statement)

References 35 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Many methods have been found to solve the exact solution of NLS equation, such as Hirota bilinear method, DT method, Riemann-Hilbert method and Bäcklund transformations [14][15][16][17][18]. As we all know, there are many research results about the exact solution of NLS equation, including rogue waves [10,11,[19][20][21][22], soliton solutions [10,23,24,52,53], breathers [15,22], rational solutions [14,25] and other localized waves [26,27].…”

Section: Introductionmentioning

confidence: 99%

Solitons, breathers and periodic rogue waves for the variable-coefficient seventh-order nonlinear Schrödinger equation

Jiang¹,

Zhaqilao

2023

Phys. Scr.

View full text Add to dashboard Cite

Through Darboux transformation (DT) method, Several nonlinear wave solutions of seventh-order variable-coefficient nonlinear Schrödinger (vcNLS) equation are obtained, including solitons, breathers and rogue periodic waves. When the coefficients are linear, parabolic and periodic functions, the parabolic, cubic and quasi-periodic solitons and breathers can be constructed. Then we investigatetheir effects on the solutions, the variation of the coefficients affects the shapes of the solutions. On this basis, the interactions between two solitons are studied and the interactions between two types of breathers are constructed. Next, through the approaches of the nonlinearization of spectral problem and DT method, rogue waves on the background of the Jacobi elliptic functions dn and cn for a seventh-order vcNLS equation are constructed. When the coefficients are selected as linear, exponential and periodic functions, the nonlinear dynamics of two kinds of rogue periodic waves are analysed.

show abstract

Section: Introductionmentioning

confidence: 99%

Solitons, breathers and periodic rogue waves for the variable-coefficient seventh-order nonlinear Schrödinger equation

Jiang¹,

Zhaqilao

2023

Phys. Scr.

View full text Add to dashboard Cite

show abstract

Painlevé Analysis and Soliton Solutions for an Inhomogeneous Heisenberg Ferromagnetic System

Wang,

2024

J Nonlinear Math Phys

View full text Add to dashboard Cite

In this paper we investigate an inhomogeneous higher-order nonlinear Schrödinger equation generated from the deformation of an inhomogeneous Heisenberg ferromagnetic system. Considering the variable coefficients from the inhomogeneities in the ferromagnetic medium, we present the Painlevé-integrable condition. Introducing an auxiliary function, we obtain the one-, two-and N-soliton solutions via the Hirota method. Furthermore, we graphically analyze the influence of inhomogeneities on the soliton propagation and interaction. It is found that the inhomogeneities will cause an increasing-decreasing process of soliton amplitude, and the change of the propagation direction. The perturbation terms can affect the propagation region of soliton but have no influence on the soliton amplitude. We consider the interactions between/among two and three solitons with the same or different initial propagation directions, and observe that the inhomogeneities can influence the soliton amplitudes and propagation directions, while the perturbation parameter can only affect the propagation direction of the soliton. In addition, bound state of solitons and its interaction with soliton are analyzed under the given excitation condition.

show abstract

Rogue wave solutions for the generalized fifth-order nonlinear Schrödinger equation on the periodic background

Wang

Zhaqilao

2022

Wave Motion

View full text Add to dashboard Cite

Rogue Wave Solutions and Generalized Darboux Transformation for an Inhomogeneous Fifth-Order Nonlinear Schrödinger Equation

Cited by 4 publications

References 35 publications

Solitons, breathers and periodic rogue waves for the variable-coefficient seventh-order nonlinear Schrödinger equation

Solitons, breathers and periodic rogue waves for the variable-coefficient seventh-order nonlinear Schrödinger equation

Painlevé Analysis and Soliton Solutions for an Inhomogeneous Heisenberg Ferromagnetic System

Rogue wave solutions for the generalized fifth-order nonlinear Schrödinger equation on the periodic background

Contact Info

Product

Resources

About