- Wen-Xiu Ma is Professor of Mathematics at University of South Florida, USA. He received his undergraduate degree from... moreWen-Xiu Ma is Professor of Mathematics at University of South Florida, USA. He received his undergraduate degree from University of Science and Technology of China, Hefei, in 1982, and earned his Ph.D. from Computer Center of Chinese Academy of Sciences in Beijing, China, in 1990. He received a youth award from the International Mathematical Union in 1993, the Alexander-von Humboldt research fellowship in Germany in 1993, and the Shanghai Government Qimingxing fellowship in 1994, the Extraordinary University Professorship of North-West University, South Africa from 2017, Oversea Distinguished Professor of King Abdulaziz University, Saudi Arabia and Zhejiang Normal University, China from 2018, Chair Professor of South China University of Technology, China from 2019, USF outstanding faculty award in 2018 and 2020, and Albert Nelson Marquis Lifetime Achievement Award, USA in 2018. He has made Clarivate’s highly cited researchers list since 2015 (hcr.clarivate.com). He is currently editor-in-chief of Journal of Applied Mathematics and Physics, Asian Journal of Mathematics and Physics, International Journal of Engineering Mathematics and Physics, International Journal of Complexity, and Partial Differential Equations in Applied Mathematics.edit
Research Interests: Mathematics and Hierarchy
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We construct matrix integrable fourth-order nonlinear Schrödinger equations through reducing the Ablowitz–Kaup–Newell–Segur matrix eigenvalue problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the... more
We construct matrix integrable fourth-order nonlinear Schrödinger equations through reducing the Ablowitz–Kaup–Newell–Segur matrix eigenvalue problems. Based on properties of eigenvalue and adjoint eigenvalue problems, we solve the corresponding reflectionless Riemann–Hilbert problems, where eigenvalues could equal adjoint eigenvalues, and formulate their soliton solutions via those reflectionless Riemann–Hilbert problems. Soliton solutions are computed for three illustrative examples of scalar and two-component integrable fourth-order nonlinear Schrödinger equations.
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The aim of this paper is to construct a six-component integrable hierarchy associated with a matrix spatial spectral problem of arbitrary order. The adopted method is the zero curvature formulation. The corresponding Hamiltonian... more
The aim of this paper is to construct a six-component integrable hierarchy associated with a matrix spatial spectral problem of arbitrary order. The adopted method is the zero curvature formulation. The corresponding Hamiltonian formulation is furnished by using the trace identity, which guarantees the Liouville integrability for the resulting hierarchy. Two illustrative examples of integrable equations of lower orders are six-component coupled nonlinear Schrödinger equations and modified Korteweg–de Vries equations.
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We analyze N-soliton solutions and explore the Hirota N-soliton conditions for scalar (1 + 1)-dimensional equations, within the Hirota bilinear formulation. An algorithm to verify the Hirota conditions is proposed by factoring out common... more
We analyze N-soliton solutions and explore the Hirota N-soliton conditions for scalar (1 + 1)-dimensional equations, within the Hirota bilinear formulation. An algorithm to verify the Hirota conditions is proposed by factoring out common factors out of the Hirota function in N wave vectors and comparing degrees of the involved polynomials containing the common factors. Applications to a class of generalized KdV equations and a class of generalized higher-order KdV equations are made, together with all proofs of the existence of N-soliton solutions to all equations in two classes.
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Explicit and exact travelling wave solutions are presented for a seventh odder generalized KdV equation, which also provides evidence for a qualitative analysis by Pomeau et al. Moreover its two-dimensional generalization is discussed.... more
Explicit and exact travelling wave solutions are presented for a seventh odder generalized KdV equation, which also provides evidence for a qualitative analysis by Pomeau et al. Moreover its two-dimensional generalization is discussed. ... 2. K. Kakutani and H. Ono J. Phys. ...
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The deformation theory, in Ref [5],of travelling wave solutions to a generalized KdV equation is modified. The necessary and sufficient condition for a relevant algebraic equation to possess nonzero real root is presented and thus an... more
The deformation theory, in Ref [5],of travelling wave solutions to a generalized KdV equation is modified. The necessary and sufficient condition for a relevant algebraic equation to possess nonzero real root is presented and thus an error of analyses in Ref. [5] is pointe-dont. Finally an explicit formula of the solitary wave solutions generated by deformetion theory is obtained directly from the generalized KdV equation itselp.
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A linear superposition is studied for Wronskian rational solutions to the KdV equation, which include rogue wave solutions. It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian... more
A linear superposition is studied for Wronskian rational solutions to the KdV equation, which include rogue wave solutions. It is proved that it is equivalent to a polynomial identity that an arbitrary linear combination of two Wronskian polynomial solutions with a difference two between the Wronskian orders is again a solution to the bilinear KdV equation. It is also conjectured that there is no other rational solutions among general linear superpositions of Wronskian rational solutions.
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Abstract We consider a linear combination of the potential KP equation and the BKP equation, and call it a combined pKP–BKP equation. We prove that the combined pKP–BKP equation satisfies the Hirota N -soliton condition and thus it... more
Abstract We consider a linear combination of the potential KP equation and the BKP equation, and call it a combined pKP–BKP equation. We prove that the combined pKP–BKP equation satisfies the Hirota N -soliton condition and thus it possesses an N -soliton solution. The proof is an application of an algorithm to compare degrees of homogeneous polynomials associated with the Hirota function in N wave vectors.
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... Printed in the UK LElTER TO THE EDITOR An approach for constructing non-isospectral hierarchies of evolution equations Wen-xiu Ma CCAST (World Laboratory) PO Box 8730, Beijing. 100080, People's Republic of China and (mailing... more
... Printed in the UK LElTER TO THE EDITOR An approach for constructing non-isospectral hierarchies of evolution equations Wen-xiu Ma CCAST (World Laboratory) PO Box 8730, Beijing. 100080, People's Republic of China and (mailing address) Institute of Mathematics. ...
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ABSTRACT
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A matrix spectral problem is researched with an arbitrary parameter. Through zero curvature equations, two hierarchies are constructed of isospectral and nonisospectral generalized derivative nonlinear schrödinger equations. The resulting... more
A matrix spectral problem is researched with an arbitrary parameter. Through zero curvature equations, two hierarchies are constructed of isospectral and nonisospectral generalized derivative nonlinear schrödinger equations. The resulting hierarchies include the Kaup-Newell equation, the Chen-Lee-Liu equation, the Gerdjikov-Ivanov equation, the modified Korteweg-de Vries equation, the Sharma-Tasso-Olever equation and a new equation as special reductions. The integro-differential operator related to the isospectral and nonisospectral hierarchies is shown to be not only a hereditary but also a strong symmetry of the whole isospectral hierarchy. For the isospectral hierarchy, the corresponding τ -symmetries are generated from the nonisospectral hierarchy and form an infinite-dimensional symmetry algebra with the K-symmetries.