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A new high-order spectral problem of the mKdV and its associated integrable decomposition

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Chinese Physics B 2007年第2期16卷 296-302页

作者：季杰姚玉芹虞静刘玉清 Department of Mathematics Shanghai University Shanghai 200444 China Department of Mathematics University of Science and Technology of China Hefei 230026 China Department of Information Science Jiangsu Polytechnic University Changzhou 213016 China

A new approach to formulizing a new high-order matrix spectral problem from a normal 2 × 2 matrix modified Korteweg-de Vries （mKdV） spectral problem is presented. It is found that the isospectral evolution equation hierarchy of this new higher-order matrix spectral problem turns out to be the well-known mKdV equation hierarchy. By using the binary nonlinearization method, a new integrable decomposition of the mKdV equation is obtained in the sense of Liouville. The proof of the integrability shows that r-matrix structure is very interesting,

关键词： spectral problem integrable decomposition mKdV equation hierarchy

Decomposition of Soliton Hierarchy Associated with a Schrodinger Type spectral problem

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Chinese Quarterly Journal of Mathematics 2008年第3期23卷 453-457页

作者： XING Xiu-zhi WU Jing-zhu GENG Xian-guo Department of Mathematics Zhoukou Normal University Zhoukou 466000 China Department of Mathematics Zhengzhou University Zhengzhou 450052 China

The soliton hierarchy associated with a Schrodinger type spectral problem with four potentials is decomposed into a class of new finite-dimensional Hamiltonian systems by using the nonlinearized approach. It is worth to point that the solutions for the soliton hierarchy are reduced to solving the compatible Hamiltonian systems of ordinary differential equations.

关键词： soliton hierarchy spectral problem Hamiltonian system

A New m × m Matrix Kaup-Newell spectral problem and Its Associated Integrable Decomposition

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Northeastern Mathematical Journal 2007年第2期23卷 141-150页

作者：张建兵季杰刘玉清姚玉芹 Department of Mathematics Shanghai University Shanghai 200444 School of Mathematical Sciences Xuzhou Normal University Xuzhou 221116 Department of Information Science Jiangsu Polytechnic University Ghangzhou 213016

A new m × m matrix Kaup-Newell spectral problem is constructed from a normal 2 × 2 matrix Kaup-Newell spectral problem, a new integrable decomposition of the Kaup-Newell equation is presented. Through this process, ... 详细信息

关键词： spectral problem Kaup-Newell equation hierarchy integrable decomposition

Almost Regularity Conditions of spectral problems for a Second Order Equation

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Communications in Theoretical Physics 2004年第5期41卷 649-654页

作者： Yu.A.Mamedov H.I.Ahmadov Faculty of Applied Mathematics and Cybernetics Baku State University370148 BakuAzerbaijan

The asymptotic distributions are exactly solved for linearly independent solutions considering problem of the second order and for the coefficients of asymptotic distribution the recurrent formulas are obtained. Further, using obtained recurrent formulas the necessary and sufficient conditions for almost regularity of spectral problem for the equation of the second order is proved.

关键词： spectral problem asymptotic distribution

Numerical Approximation of an Axisymmetric Elastoacoustic Eigenvalue problem

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Communications in Computational Physics 2023年第10期34卷 1420-1438页

作者： J.Querales P.Venegas GIMNAP Departamento de MatematicaUniversidad del Bio-BioConcepcionChile Departamento de Ciencias Exactas Facultad de IngenieriaArquitectura y DisenoUniversidad San SebastianConcepcionChile

This paper deals with the numerical approximation of a pressure/displacement formulation of the elastoacoustic vibration problem in the axisymmetric *** propose and analyze a discretization based on Lagrangian finite elements in the fluid and solid *** show that the scheme provides a correct approximation of the spectrum and prove quasi-optimal error *** report numerical results to validate the proposed methodology for elastoacoustic vibrations.

关键词： Axisymmetric problem fluid-structure interaction spectral problem finite element method

An extension of the modified Sawada-Kotera equation and conservation laws

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Chinese Physics B 2012年第7期21卷 37-42页

作者：何国亮耿献国 Department of Mathematics Zhengzhou University Department of Mathematics and Information Science Zhengzhou University of Light Industry

Based on the modified Sawad^Kotera equation, we introduce a 3 ~ 3 matrix spectral problem with two potentials and derive a hierarchy of new nonlinear evolution equations. The second member in the hierarchy is a generalization of the modified Sawad-Kotera equation, by which a Lax pair of the modified Sawada-Kotera equation is obtained. With the help of the Miura transformation, explicit solutions of the Sawad-Kotera equation, the Kaup-Kupershmidt equation, and the modified Sawad-Kotera equation are given. Moreover, infinite sequences of conserved quantities of the first two nonlinear evolution equations in the hierarchy and the modified Sawada-Kotera equation are constructed with the aid of their Lax pairs.

关键词： spectral problem explicit solutions conservation laws

Riemann-Hilbert approach of the complex Sharma-Tasso-Olver equation and its N-soliton solutions

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Chinese Physics B 2023年第4期32卷 130-134页

作者：李莎夏铁成魏含玉 Department of Mathematics Shanghai UniversityShanghai 200444China College of Mathematics and Statistics Zhoukou Normal UniversityZhoukou 466001China

We study the complex Sharma-Tasso-Olver equation using the Riemann-Hilbert *** associated Riemann-Hilbert problem for this integrable equation can be naturally constructed by considering the spectral problem of the Lax ***,in the case that the Riemann-Hilbert problem is irregular,the N-soliton solutions of the equation can be *** addition,the three-dimensional graphic of the soliton solutions and wave propagation image are graphically depicted and further discussed.

关键词： complex Sharma-Tasso-Olver equation Riemann-Hilbert problem spectral problem soliton solutions

Flat Solutions of Some Non-Lipschitz Autonomous Semilinear Equations May be Stable for N≥3

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Chinese Annals of Mathematics,Series B 2017年第1期38卷 345-378页

作者： Jesús Ildefonso DIAZ Jesús HERNaNDEZ Yavdat IL'Y ASOV Instituto de Matematica Interdisciplinar Universidad Complutense de Madrid 28040 MadridSpain. Departamento de Matematicas Universidad Autonoma de Madrid 28049 CantoblancoMadridSpain. Institute of Mathematics Ufa Science Center of RAS 112Chernyshevsky StrUfa 450077Russia.

The authors prove that flat ground state solutions(i.e. minimizing the energy and with gradient vanishing on the boundary of the domain) of the Dirichlet problem associated to some semilinear autonomous elliptic equations with a strong absorption term given by a non-Lipschitz function are unstable for dimensions N = 1, 2 and they can be stable for N ≥ 3 for suitable values of the involved exponents.

关键词： Semilinear elliptic and parabolic equation Strong absorption spectral problem Nehari manifolds Pohozaev identity Flat solution Linearized stability Lyapunov function Global instability

A Hierarchy of Differential-Difference Equations and Their Integrable Couplings

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Chinese Physics Letters 2007年第6期24卷 1444-1447页

作者：罗琳范恩贵 School of Mathematics Fudan University Shanghai 200433 Department of Mathematics Xiaogan University Xiaogan 432100

Starting from a discrete spectral problem, the corresponding hierarchy of nonlinear differential-difference equation is proposed. It is shown that the hierarchy possesses the bi-Hamiltionian structures. Further, two i... 详细信息

关键词： SOLITON-EQUATIONS spectral problem SYSTEMS