Compactification of Patterns by a Singular Convection or Stress
- School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978 (Israel)
A wide variety of propagating disturbances in physical systems are described by equations whose solutions lack a sharp propagating front. We demonstrate that presence of particular nonlinearities may induce such fronts. To exemplify this idea, we study both dissipative u{sub t}+{partial_derivative}{sub x}f(u)=u{sub xx} and dispersive u{sub t}+{partial_derivative}{sub x}f(u)+u{sub xxx}=0 patterns, and show that a weakly singular convection f(u)=-u{sup {alpha}}+u{sup m}, 0<{alpha}<1<m, induces a sharp localization of fronts around the u=0 ground state. Notably, a sharp front also emerges in higher dimensional extensions: u{sub t}+{partial_derivative}{sub x}[f(u)+{nabla}{sup 2}u]=0 or in wave phenomena of the Boussinesq type: Z{sub tt}={nabla}{center_dot}[F{sub *}(|{nabla}Z|){nabla}Z]-{nabla}{sup 4}Z where F{sub *}({sigma})=C{sup 2}{sigma}+f({sigma})
- OSTI ID:
- 21024539
- Journal Information:
- Physical Review Letters, Journal Name: Physical Review Letters Journal Issue: 23 Vol. 99; ISSN 0031-9007; ISSN PRLTAO
- Country of Publication:
- United States
- Language:
- English
Similar Records
A Dynamical System Associated with Newton's Method for Parametric Approximations of Convex Minimization Problems
Final state problem for the cubic nonlinear Klein-Gordon equation