## Conservation laws for nonlinear telegraph equations.(English)Zbl 1077.35087

The authors give the complete conservation law classification for nonlinear telegraph systems of the form $H_1[u,v]=v_t-F(u)u_x-G(u)=0, H_2[u,v]=u_t-v_x=0,\tag{1}$ with respect to a class of multipliers that are functions of the independent and dependent variables of the system. It is shown that a large class of nonlinear telegraph systems possesses four local conservation laws. The pairs of $$F(u),G(u)$$ admitting conservation laws together with corresponding multipliers, fluxes and densities are presented in tables.
Reviewer’s remarks: The complete point symmetry classification of the system (1) is given in [G. W. Bluman, Temuerchaolu and R. Sahadevan, Local and nonlocal symmetries for nonlinear telegraph equations, J. Math. Phys. 46, No. 2, 023505 (2005; Zbl 1076.35077)], where the classification of the conservation laws of (1) for various forms of $$F(u)$$ and $$G(u)$$ is not presented.

### MSC:

 35L65 Hyperbolic conservation laws 35A30 Geometric theory, characteristics, transformations in context of PDEs

### Keywords:

complete classification

Zbl 1076.35077
Full Text:

### References:

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