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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

Citations:

Zbl 1076.35077
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References:

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