Journal of Nonlinear Mathematical Physics
Volume 24, Issue 1, December 2016
Letter to Editor
Pages: 1 - 6
A simple application of a neat formula relating the time evolution of the N zeros of a (monic) time-dependent polynomial of degree N in the complex variable w to the time evolution of its N coefficients allows to identify integrable Hamiltonian N-body problems in the plane featuring N arbitrary functions,...
2. Miura and auto-Backlund transformations for the q-deformed KP and q-deformed modified KP hierarchies
Pages: 7 - 19
The Miura and anti-Miura transformations between the q-deformed KP and the q-deformed modified KP hierarchies are investigated in this paper. Then the auto-Backlund transformations for the q-deformed KP and q-deformed modified KP hierarchies are constructed through the combinations of the Miura and anti-Miura...
Pages: 20 - 28
New periodic solutions of signum-Gordon equation are presented. We first find solutions φ0(x, t) defined for (x, t) ∈ ℝ × [0, T ] and satisfying the condition φ0(x, 0) = φ0(x, T ) = 0. Then these solutions are extended to the whole spacetime by using (2.4).
Eric Tovar, Haicheng Gu, Zhijun Qiao
Pages: 29 - 40
In this paper, we study a (2 + 1)-dimensional generalized Camassa-Holm (2dgCH) equation with both quadratic and cubic nonlinearity. We derive a peaked soliton (peakon) solution, double-peakon solutions, and kink-peakon solutions. In particular, weak kink - peakon solution is the first time to address...
Orest D. Artemovych, Denis Blackmore, Anatolij K. Prykarpatski
Pages: 41 - 72
A general differential-algebraic approach is devised for constructing multi-component Hamiltonian operators as differentiations on suitably constructed loop Lie algebras. The related Novikov-Leibniz algebraic structures are presented and a new non-associative “Riemann” algebra is constructed, which is...
Matthew Babela, Alexandre Odesskii
Pages: 73 - 78
We construct a family of integrable equations of the form vt = f(v; vx; vxx; vxxx) such that f is a transcendental function in v; vx; vxx. This family is related to the Krichever-Novikov equation by a differential substitution. Our construction of integrable equations and the corresponding differential...
Qiufang Liu, Chuanzhong Li
Pages: 79 - 92
In this paper, we construct the noncommutative B and C type KP hierarchies using pseudo-differential operators and reducing conditions. Further a series of additional flows of the noncommutative B and C type KP hierarchies will be defined and the additional symmetries constitute the B and C type infinite...
Xiao-yan Tang, Zu-feng Liang
Pages: 93 - 106
Nonlocal symmetries of the (1+1)-dimensional Sinh-Gordon (ShG) equation are obtained by requiring it, together with its Bäcklund transformation (BT), to be form invariant under the infinitesimal transformation. Naturally, the spectrum parameter in the BT enters the nonlocal symmetries, and thus through...
9. Bilinearization and soliton solutions of N=1 supersymmetric coupled dispersionless integrable system
Arifa Mirza, Mahmood ul Hassan
Pages: 107 - 115
An N=1 supersymmetric generalization of coupled dispersionless (SUSY-CD) integrable system has been proposed by writing its superfield Lax representation. It has been shown that under a suitable variable transformation, the SUSY-CD integrable system is equivalent to N=1 supersymmetric sine-Gordon equation....
10. New Double Wronskian Solutions of the Whitham-Broer-Kaup System: Asymptotic Analysis and Resonant Soliton Interactions
Tao Xu, Changjing Liu, Fenghua Qi, Chunxia Li, Dexin Meng
Pages: 116 - 141
In this paper, by the Darboux transformation together with the Wronskian technique, we construct new double Wronskian solutions for the Whitham-Broer-Kaup (WBK) system. Some new determinant identities are developed in the verification of the solutions. Based on analyzing the asymptotic behavior of new...
Pages: 142 - 148
A technique to identify new C-integrable and S-integrable systems of nonlinear partial differential equations is reported, with two representative examples displayed and tersely discussed.