Classical Completely Integrable System Generated through Nonlinearization of an Eigenvalue Problem

Chinese Quarterly Journal of Mathematics ›› 2004, Vol. 19 ›› Issue (3): 323-330.

Department of Compute Science, Henan Institute of Finance and Economics, Zhengzhou 450002, China; Department of Information Engineering, North China Institute of Water Conservancy and Hydroelectric Power, Zhengzhou 450008, China; National Key Laboratory, on ISN, Xidian University,Xi 'an 710071, China

Received:2004-05-26 Online:2004-09-30 Published:2024-03-14
About author:LUO Man(1968-),female,native of Xinhua,Hunan,a lecturer of Henan Institute of Finance and Economics,M.S.D,engages in soliton theory.

Abstract

Abstract: Under the Bargmann constrained condition, the spatial part of a new Lax pair of the higher order MkdV equation is nonlinearized to be a completely integrable system (R^2N,dp^dq, H₀=1/2F₀)(F0= (^q,p) + (^p,p) + (p,q)²). While the nonlinearization of the time part leads to its N-involutive system (F_m).

Key words: integrable , , system, nonlinearization, involutive , , solution

CLC Number:

O175.3

LUO Man, LI Xiu-li, XIANG Ming-sen. Classical Completely Integrable System Generated through Nonlinearization of an Eigenvalue Problem[J]. Chinese Quarterly Journal of Mathematics, 2004, 19(3): 323-330.

[1]	ZOU Mian-lu, LI Qiang. Some New Regularity Criteria for the 3D Boussinesq Equations in Homogeneous Besov Spaces [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 73-81.
[2]	LIU Gong-wei, YANG Kun. Finite Time Blow-Up and Global Existence for Degenerate Parabolic Equations at High Initial Energy [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 97-110.
[3]	TANG Zhong-hua, FANG Shao-mei. Implicit Finite Difference Method for Time-Space Caputo-Riesz Fractional Diffusion Equation with Fractional Robin Boundary Conditions [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 18-30.
[4]	LI Hong-jun. Hopf-Rinow Theorem on Convex Complex Finsler Manifolds [J]. Chinese Quarterly Journal of Mathematics, 2024, 39(1): 31-45.
[5]	PAN Jia-hui, FANG Shao-mei. Initial Boundary Value Problem for Pseudo-Parabolic p-Laplacian Type Equation with Logarithmic Nonlinearity [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 360-369.
[6]	XU Na. The Existence of Ground State Solutions for a Class of Sublinear Kirchhoff Equations [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 410-414.
[7]	SUN Xiao-lei. Competitive Equilibrium of Central Bank Digital Currency and Private Cryptocurrency: A Perspective of Regulatory [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 415-423.
[8]	WANG Ke, PAN Pan-pan. Exact Boundary Controllability for a 1-D Second-Order Quasilinear Hyperbolic System [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(4): 424-440.
[9]	YANG Yi-song. Some Applications of Surface Curvatures in Theoretical Physics [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 221-253.
[10]	GUAN Daniel. Some Applications of Group Actions in Complex Geometry [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 254-275.
[11]	QIN Yu-ming, CHEN Jia-le, JIANG Hui-te. A New Existence Theorem for Global Attractors and its Application to a Non-Classical Diffusion Equation [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 276-289.
[12]	WANG Shu, SUN Rui. Global Well-Posedness of the Initial-Boundary Value Problem on Incompressible MHD-Boussinesq Equations with Nonlinear Boundary Conditions [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 290-310.
[13]	XU Xiao-meng. On the Stokes Phenomenon and Representation Theory of Quantum Groups [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(3): 311-330.
[14]	DONG Chang-zhou, LI Hao-xue. The Least Squares {P,Q,k+1}-Reflexive Solution to a Matrix Equation [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(2): 210-220.
[15]	MA Teng. Multilinear Calderón-Zygmund Operators with Kernels of#br# Dini Type and Commutators in Variable Exponent#br# Central Morrey Spaces [J]. Chinese Quarterly Journal of Mathematics, 2023, 38(2): 184-195.

Classical Completely Integrable System Generated through Nonlinearization of an Eigenvalue Problem

PDF (PC)

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments