Journal of Nonlinear Mathematical Physics

Volume 19, Issue 1, March 2012
Research Article

1. The AKNS Hierarchy Revisited: A Vertex Operator Approach and its Lie-Algebraic Structure

Denis Blackmore, Anatoliy K. Prykarpatsky
Pages: 1 - 15
A novel approach — based upon vertex operator representation — is devised to study the AKNS hierarchy. It is shown that this method reveals the remarkable properties of the AKNS hierarchy in relatively simple, rather natural and particularly effective ways. In addition, the connection of this vertex...
Research Article

2. A Direct procedure on the Integrability of Nonisospectral and Variable-Coefficient MKdV Equation

Xiaorui Hu, Yong Chen
Pages: 16 - 26
An elementary and systematic method based on binary Bell polynomials is applied to nonisospectral and variable-coefficient MKdV (vcMKdV) equation. The bilinear representation, bilinear Bäcklund transformation, Lax pair and infinite local conservation laws are obtained step by step, without too much clever...
Research Article

3. On the Recursion Operator for the Noncommutative Burgers Hierarchy

Sandra Carillo, Cornelia Schiebold
Pages: 27 - 37
The noncommutative Burgers recursion operator is constructed via the Cole–Hopf transformation, and its structural properties are studied. In particular, a direct proof of its hereditary property is given.
Research Article

4. High-Frequency Asymptotics for the Helmholtz Equation in a Half-Plane

Min-Hai Huang
Pages: 38 - 47
Base on the integral representations of the solution being derived via Fokas' transform method, the high-frequency asymptotics for the solution of the Helmholtz equation, in a half-plane and subject to the Neumann condition is discussed. For the case of piecewise constant boundary data, full asymptotic...
Research Article

5. Solutions and Lax Pairs based on Bilinear Bäcklund Transformations of Some Supersymmetric Equations

Lin Huang, Da-Jun Zhang
Pages: 48 - 61
The paper investigates solutions and Lax pairs through bilinear Bäcklund transformations for some supersymmetric equations. We derive variety of solutions from the known bilinear Bäcklund transformations. Besides, using the gauge invariance of (super) Hirota bilinear derivatives we may get deformed bilinear...
Research Article

6. New Solvable Many-Body Model of Goldfish Type

F. Calogero
Pages: 62 - 80
A new solvable N-body model of goldfish type is identified. Its Newtonian equations of motion read as follows: z¨n=-6z˙nzn-4zn3+32(z˙n+2zn2)∑k=1N(z˙ kzk+2zk)+2∑𝓁=1,𝓁≠nN[(z˙n+2zn2)(z˙𝓁+2z𝓁2)zn-z𝓁],      n=1,…,N, where...
Research Article

7. Nambu Bracket Formulation of Nonlinear Biochemical Reactions Beyond Elementary Mass Action Kinetics

T. D. Frank
Pages: 81 - 97
We develop a Nambu bracket formulation for a wide class of nonlinear biochemical reactions by exploiting previous work that focused on elementary biochemical mass action reactions. To this end, we consider general reaction mechanisms including for example enzyme kinetics. Furthermore, we go beyond elementary...
Research Article

8. Steady Internal Water Waves with a Critical Layer Bounded by the Wave Surface

Anca-Voichita Matioc
Pages: 98 - 118
In this paper we construct small amplitude periodic internal waves traveling at the boundary region between two rotational and homogeneous fluids with different densities. Within a period, the waves we obtain have the property that the gradient of the stream function associated to the fluid beneath the...
Research Article

9. Focusing mKdV Breather Solutions with Nonvanishing Boundary Condition by the Inverse Scattering Method

Miguel A. Alejo
Pages: 119 - 135
Using the Inverse Scattering Method with a nonvanishing boundary condition, we obtain an explicit breather solution with nonzero vacuum parameter b of the focusing modified Korteweg–de Vries (mKdV) equation. Moreover, taking the limiting case of zero frequency, we obtain a generalization of the double...