SOLITARY WAVE AND SIMILARITY SOLUTIONS OF THE COMBINED KdV EQUATION

Applied Mathematics and Mechanics (English Edition) ›› 1988, Vol. 9 ›› Issue (3): 311-316.

• Articles • Previous Articles

SOLITARY WAVE AND SIMILARITY SOLUTIONS OF THE COMBINED KdV EQUATION

Pan Xiu-de

Zheijing University, Hangzhou

Received:1986-12-26 Online:1988-03-18 Published:1988-03-18

Abstract

Abstract: In this paper, we discuss a property of solitary wave solutions of the combined KdV equation. Meantime, we point out that the combined KdV equation can be reduced to the Painleve equation. Furthermore, utilizing special transformations of similarity variables, we derive a kind of new partial differential equations.

Key words: plane elasticity problem, Hamiltonian system, symplectic orthogonality, eigenfunction expansion, Hamiltonian operator

Pan Xiu-de . SOLITARY WAVE AND SIMILARITY SOLUTIONS OF THE COMBINED KdV EQUATION. Applied Mathematics and Mechanics (English Edition), 1988, 9(3): 311-316.

[1]	Yongfang WEI, Suiming SHANG, Zhanbing BAI. Solutions for a class of Hamiltonian systems on time scales with non-local boundary conditions [J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(4): 587-602.
[2]	Weipeng HU, Mingzhe SONG, Zichen DENG. Structure-preserving properties of Störmer-Verlet scheme for mathematical pendulum [J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(9): 1225-1232.
[3]	Qingrui MENG, Dongqiang LU. Hydroelastic interaction between water waves and thin elastic plate floating on three-layer fluid [J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(4): 567-584.
[4]	Yi WEI, Zichen DENG, Qingjun LI, Bo WANG. Projected Runge-Kutta methods for constrained Hamiltonian systems [J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(8): 1077-1094.
[5]	Minghui FU, Kelang LU, Weihua LI, S. V. SHESHENIN. New way to construct high order Hamiltonian variational integrators [J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(8): 1041-1052.
[6]	Dong-jiao WANG;Shou-qiang QIU;Jia-wei YE. Width effects on hydrodynamics of pendulum wave energy converter [J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(9): 1167-1176.
[7]	Yu-yue QIN;Zi-chen DENG;Wei-peng HU. Structure-preserving properties of three differential schemes for oscillator system [J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(6): 783-790.
[8]	Shu-fang HU;Chuan-miao CHEN. Runge-Kutta method, finite element method, and regular algorithms for Hamiltonian system [J]. Applied Mathematics and Mechanics (English Edition), 2013, 34(6): 747-760.
[9]	WANG Hua;ALATANCANG;HUANG Jun-Jie. Completeness of system of root vectors of upper triangular infinitedimensional Hamiltonian operators appearing in elasticity theory [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(3): 385-398.
[10]	EBURILITU;ALATANCANG. Eigenfunction expansion method of upper triangular operator matrix and application to two-dimensional elasticity problems based on stress formulation [J]. Applied Mathematics and Mechanics (English Edition), 2012, 33(2): 223-232.
[11]	LI Can-Hua;CHEN Chuan-Miao. Ultraconvergence for averaging discontinuous finite elements and its applications in Hamiltonian system [J]. Applied Mathematics and Mechanics (English Edition), 2011, 32(7): 943-956.
[12]	HUANG Jun-Jie;Alatancang;WANG Hua. Eigenfunction expansion method and its application to two-dimensional elasticity problems based on stress formulation [J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(8): 1039-1048.
[13]	HOU Guo-Lin;Alatancang. Symplectic eigenfunction expansion theorem for elasticity of rectangular planes with two simply-supported opposite sides [J]. Applied Mathematics and Mechanics (English Edition), 2010, 31(10): 1241-1250.
[14]	LI Wen-cheng;DENG Zi-chen;. Adaptive explicit Magnus numerical method for nonlinear dynamical systems [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(9): 1111-1118 .
[15]	XU Xin-sheng;WANG Ga-ping;SUN Fa-ming. Analytical and numerical methods of symplectic system for Stokes flow [J]. Applied Mathematics and Mechanics (English Edition), 2008, 29(6): 705-714 .

SOLITARY WAVE AND SIMILARITY SOLUTIONS OF THE COMBINED KdV EQUATION

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 15

Recommended Articles

Metrics

Comments