Browsing by Author "Ma, Wen-Xiu"
Now showing items 1-18 of 18
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A note on rational solutions to a Hirota-Satsuma-like equation
(Elsevier, 2016)With the generalized bilinear operators based on a prime number p = 3, a Hirota-Satsuma-like equation is proposed. Rational solutions are generated and graphically described by using symbolic computation software Maple. -
A unified inverse scattering transformation for the local and nonlocal nonautonomous Gross-Pitaevskii equations
(AIP, 2017)We present the inverse scattering transformation for a nonisospectral AKNS hierarchy in which the spectral parameter is determined by an ordinary differential equation with polynomial nonlinearity, and thus, we give a ... -
Abundant interaction solutions of the KP equation
(SpringerSpringer, 2017)Based on the Hirota bilinear form of the KP equation, five classes of interaction solutions between lumps and line solitons are generated via Maple symbolic computations. Analyticity is automatically guaranteed for the ... -
An integrable generalization of the super AKNS hierarchy and its bi-Hamiltonian formulation
(Elsevier, 2017)Based on a Lie super-algebra B(0, 1), an integrable generalization of the super AKNS iso-spectral problem is introduced and its corresponding generalized super AKNS hierarchy is generated. By making use of the super-trace ... -
Applications of linear superposition principle to resonant solitons and complexitons
(Elsevier, 2017)We apply the linear superposition principle to Hirota bilinear equations and generalized bilinear equations. By extending the linear superposition principle to complex field, we construct complex exponential wave function ... -
Bäcklund transformation, multiple wave solutions and lump solutions to a (3 + 1)-dimensional nonlinear evolution equation
(SpringerSpringer, 2017)In this paper, a (3+1)-dimensional nonlinear evolution equation is cast into Hirota bilinear form with a dependent variable transformation. A bilinear Bäcklund transformation is then presented, which consists of six bilinear ... -
Binary Darboux transformation for the coupled Sasa-Satsuma equations
(AIP Publishing, 2017)The binary Darboux transformation method is applied to the coupled Sasa-Satsuma equations, which can be used to describe the propagation dynamics of femtosecond vector solitons in the birefringent fibers with third-order ... -
Classifying bilinear differential equations by linear superposition principle
(World Scientific Publishing, 2016)In this paper, we investigate the linear superposition principle of exponential traveling waves to construct a sub-class of N-wave solutions of Hirota bilinear equations. A necessary and sufficient condition for Hirota ... -
Complexiton solutions to soliton equations by the Hirota method
(AIP Publishing, 2017)We apply the Hirota direct method to construct complexiton solutions (complexitons). The key is to use Hirota bilinear forms. We prove that taking pairs of conjugate wave variables in the 2N-soliton solutions generates ... -
Darboux transformation and solitons for an integrable nonautonomous nonlinear integro-differential Schrödinger equation
(World Scientific, 2017)By modifying the scheme for an isospectral problem, the non-isospectral Ablowitz-Kaup-Newell-Segur (AKNS) hierarchy is constructed via allowing the time varying spectrum. In this paper, we consider an integrable nonautonomous ... -
Envelope bright- and dark-soliton solutions for the Gerdjikov Ivanov model
(Springer, 2015)Within the context of the Madelung fluid description, investigation has been carried out on the connection between the envelope soliton-like solutions of a wide family of nonlinear Schrödinger equations and the soliton-like ... -
Mixed lump-kink solutions to the BKP equation
(Elsevier, 2017)By using the Hirota bilinear form of the (2+1)-dimensional BKP equation, ten classes of interaction solutions between lumps and kinks are constructed through Maple symbolic computations beginning with a linear combination ... -
Mixed lump-kink solutions to the KP equation
(Elsevier, 2017)By using the Hirota bilinear form of the KP equation, twelve classes of lump-kink solutions are presented under the help of symbolic computations with Maple. Analyticity is naturally achieved by taking special choices of ... -
Rational solutions to an extended Kadomtsev-Petviashvili-like equation with symbolic computation
(Elsevier, 2016)Associated with the prime number p = 3, the generalized bilinear operators are adopted to yield an extended Kadomtsev-Petviashvili-like (eKP-like) equation. With symbolic computation, eighteen classes of rational solutions ... -
Solitary waves with the Madelung fluid description: a generalized derivative nonlinear Schrödinger equation
(Elsevier, 2016)WithintheframeworkoftheMadelungfluiddescription,wewillderivebrightanddark(includinggray-andblack-soliton)envelopesolutionsforageneralizedderivativenonlin-earSchrödingermodeli∂ ∂t=∂2 ∂x2+ia∂∂x(| |2 )+b| |2 ,byvirtueofthec ... -
Trigonal curves and algebro-geometric solutions to soliton hierarchies I
(Royal Society, 2017)This is the first part of a study, consisting of two parts, on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, using linear combinations of Lax matrices of soliton ... -
Trigonal curves and algebro-geometric solutions to soliton hierarchies II
(Royal Society, 2017)This is a continuation of a study on Riemann theta function representations of algebro-geometric solutions to soliton hierarchies. In this part, we straighten out all flows in soliton hierarchies under the Abel-Jacobi ... -
Two integrable Hamiltonian hierarchies in sl(2, R) and so(3, R) with three potentials
(AIP Publishing, 2017)By introducing two specific matrix spectral problems associated with sl(2,ℝ) and so(3,ℝ) matrix Lie algebras, we generate two integrable Hamiltonian hierarchies with three potentials. The computation and analysis on their ...