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Nonlinear Green’s Functions for Wave Equation with Quadratic and Hyperbolic Potentials

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  • Asatur Zh. Khurshudyan

Abstract

The advantageous Green’s function method that originally has been developed for nonhomogeneous linear equations has been recently extended to nonlinear equations by Frasca. This article is devoted to rigorous and numerical analysis of some second‐order differential equations new nonlinearities by means of Frasca’s method. More specifically, we consider one‐dimensional wave equation with quadratic and hyperbolic nonlinearities. The case of exponential nonlinearity has been reported earlier. Using the method of generalized separation of variables, it is shown that a hierarchy of nonlinear wave equations can be reduced to second‐order nonlinear ordinary differential equations, to which Frasca’s method is applicable. Numerical error analysis in both cases of nonlinearity is carried out for various source functions supporting the advantage of the method.

Suggested Citation

  • Asatur Zh. Khurshudyan, 2018. "Nonlinear Green’s Functions for Wave Equation with Quadratic and Hyperbolic Potentials," Advances in Mathematical Physics, John Wiley & Sons, vol. 2018(1).
    • Handle: RePEc:wly:jnlamp:v:2018:y:2018:i:1:n:7179160
    DOI: 10.1155/2018/7179160
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    References listed on IDEAS

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    1. Caixia Guo & Jianmin Guo & Ying Gao & Shugui Kang, 2016. "Existence of Positive Solutions for Two-Point Boundary Value Problems of Nonlinear Finite Discrete Fractional Differential Equations and Its Application," Advances in Mathematical Physics, Hindawi, vol. 2016, pages 1-9, May.
    2. Caixia Guo & Jianmin Guo & Ying Gao & Shugui Kang, 2016. "Existence of Positive Solutions for Two‐Point Boundary Value Problems of Nonlinear Finite Discrete Fractional Differential Equations and Its Application," Advances in Mathematical Physics, John Wiley & Sons, vol. 2016(1).
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