Exact Solutions of Nonlinear Telegraph Equations with Delay
https://doi.org/10.56304/S2304487X19050079
Abstract
The following nonlinear telegraph equations with delay are considered: un + H(u)ut = (G(u)ux)x + F (u, w); un = (G(u)ux)x + P(u)ux)x + F (u, w), where u = u(x, t), w = u(x, t - τ), and τ – is the constant delay time. The equations contain the nonlinear transfer coefficient G(u) of the power-law or exponential type, as well as the coefficients H(u) and P(u) that either are constant or are nonlinear and have the form similar to the form of G(u) The kinetic functions F of all the equations consist of one or several arbitrary functions of one argument. For the equations under consideration, new exact travelling-wave solutions, as well as new exact solutions with generalized and functional separation of variables, have been obtained by means of the modified method of functional constraints. All the solutions are expressed in terms of elementary functions, contain free parameters, and can be used for the formulation of test problems to assess the accuracy of numerical methods for solving nonlinear partial differential equations with delay. Publications presenting exact solutions of equations with delay and describing methods for constructing exact solutions have been reviewed.
Keywords
telegraph equations with delay,
nonlinear differential-difference equations,
exact solutions,
travelling-wave solutions,
separable solutions
Supporting agencies: The work was carried out on the topic of the state assignment (state registration No. AAAA-A17-117021310385-6)
About the Author
V. G. Sorokin
Ishlinsky Institute for Problems in Mechanics, Russian Academy of Sciences
Russian Federation
Russian Federation
119526
Moscow
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Review
For citations:
Sorokin V.G. Exact Solutions of Nonlinear Telegraph Equations with Delay. Vestnik natsional'nogo issledovatel'skogo yadernogo universiteta "MIFI". 2019;8(5):453-464. (In Russ.) https://doi.org/10.56304/S2304487X19050079
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