Singularity Analysis and Integrability of a Burgers-Type System of Foursov
نویسندگان
چکیده
We apply the Painlevé test for integrability of partial differential equations to a system of two coupled Burgers-type equations found by Foursov, which was recently shown by Sergyeyev to possess infinitely many commuting local generalized symmetries without any recursion operator. The Painlevé analysis easily detects that this is a typical C-integrable system in the Calogero sense and rediscovers its linearizing transformation.
منابع مشابه
Infinitely many local higher symmetries without recursion operator or master symmetry: integrability of the Foursov–Burgers system revisited
We consider the Burgers-type system studied by Foursov, w t = w xx + 8ww x + (2 − 4α)zz x , z t = (1 − 2α)z xx − 4αzw x + (4 − 8α)wz x − (4 + 8α)w 2 z + (−2 + 4α)z 3 , for which no recursion operator or master symmetry was known so far, and prove that this system admits infinitely many local higher symmetries that are constructed using a nonlocal two-term recursion relation rather than a recurs...
متن کاملSymmetrically coupled higher-order nonlinear Schrödinger equations: singularity analysis and integrability
The integrability of a system of two symmetrically coupled higher-order nonlinear Schrödinger equations with parameter coefficients is tested by means of the singularity analysis. It is proven that the system passes the Painlevé test for integrability only in ten distinct cases, of which two are new. For one of the new cases, a Lax pair and a multi-field generalization are obtained; for the oth...
متن کاملSolving a nonlinear inverse system of Burgers equations
By applying finite difference formula to time discretization and the cubic B-splines for spatial variable, a numerical method for solving the inverse system of Burgers equations is presented. Also, the convergence analysis and stability for this problem are investigated and the order of convergence is obtained. By using two test problems, the accuracy of presented method is verified. Additional...
متن کاملSingularity Analysis towards Nonintegrability of Nonhomogeneous Nonlinear Lattices
We show non-integrability of the nonlinear lattice of Fermi-Pasta-Ulam type via singularity analysis of normal variational equations of Lamé type. 1. From a Nonlinear Lattice to Lamé Equations We consider the following one-dimensional lattice:
متن کامل0 Symmetrically coupled higher - order nonlinear Schrödinger equations : singularity analysis and integrability
The integrability of a system of two symmetrically coupled higherorder nonlinear Schrödinger equations is tested by means of the singularity analysis. It is proven that the system passes the Painlevé test for integrability only in ten distinct cases, of which two are new. For one of the new cases, a Lax pair and a multi-field generalization are obtained; for the other one, the equations of the ...
متن کامل