Newton's method and periodic solutions of nonlinear wave equations

1993/12/01 by Walter Craig, C. Eugene Wayne · 26 citations
Physics and Astronomy · Mathematics · Engineering · #Quantum chaos and dynamical systems #Numerical methods for differential equations #Stability and Controllability of Differential Equations

paper · doi:10.1002/cpa.3160461102

Abstract

Abstract We prove the existence of periodic solutions of the nonlinear wave equation satisfying either Dirichlet or periodic boundary conditions on the interval [ O , π]. The coefficients of the eigenfunction expansion of this equation satisfy a nonlinear functional equation. Using a version of Newton's method, we show that this equation has solutions provided the nonlinearity g ( x, u ) satisfies certain generic conditions of nonresonance and genuine nonlinearity. © 1993 John Wiley & Sons, Inc.

Citations

• Periodic and quasi-periodic solutions of nonlinear wave equations via KAM theory

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