Numerical study of blow-up in solutions to generalized Kadomtsev-Petviashvili equations

DOI10.3934/dcdsb.2014.19.1689zbMath1302.35338arXiv1310.5215OpenAlexW2964116990MaRDI QIDQ478663

Ralf Peter, Christian Klein

Publication date: 4 December 2014

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1310.5215

zbMATH Keywords

blow-updynamic rescalinggeneralized Kadomtsev-Petviasvili equationsnumerical approaches

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) KdV equations (Korteweg-de Vries equations) (35Q53) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20) Blow-up in context of PDEs (35B44)

Related Items (9)

Construction of a minimal mass blow up solution of the modified Benjamin-Ono equation ⋮ Modeling ultrashort electromagnetic pulses with a generalized Kadomtsev-Petviashvili equation ⋮ On critical behaviour in generalized Kadomtsev-Petviashvili equations ⋮ Numerical study of Zakharov-Kuznetsov equations in two dimensions ⋮ On a class of derivative Nonlinear Schrödinger-type equations in two spatial dimensions ⋮ Numerical study of blow-up and stability of line solitons for the Novikov–Veselov equation ⋮ Numerical study of soliton stability, resolution and interactions in the 3D Zakharov-Kuznetsov equation ⋮ A numerical approach to Blow-up issues for Davey-Stewartson II systems ⋮ Numerical study of blow-up and dispersive shocks in solutions to generalized Korteweg-de Vries equations

Uses Software

• fminsearch

Cites Work

• Unnamed Item
• Exponential time differencing for stiff systems
• Fourth order time-stepping for low dispersion Korteweg-de Vries and nonlinear Schrödinger equations
• Asymptotics of the solitary waves for the generalized Kadomtsev-Petviashvili equations
• Computations of blow-up and decay for periodic solutions of the generalized Korteweg-de Vries-Burgers equation
• Solitary waves of generalized Kadomtsev-Petviashvili equations
• Numerical study of blow up and stability of solutions of generalized Kadomtsev-Petviashvili equations
• Numerical computations of self-similar blow-up solutions of the generalized Korteweg-de Vries equation
• Numerical study of blow-up and dispersive shocks in solutions to generalized Korteweg-de Vries equations
• Numerical study of oscillatory regimes in the Kadomtsev-Petviashvili equation
• Fourth Order Time-Stepping for Kadomtsev–Petviashvili and Davey–Stewartson Equations
• Well-posedness of the Cauchy problem for models of large amplitude internal waves
• Convergence Properties of the Nelder--Mead Simplex Method in Low Dimensions
• The Cauchy problem for the Kadomtsev–Petviashvili–I equation without the zero mass constraint
• Solutions of the KPI equation with smooth initial data
• Symmetries and Decay of the Generalized Kadomtsev--Petviashvili Solitary Waves
• Blow up and instability of solitary-wave solutions to a generalized Kadomtsev-Petviashvili equation
• Conservative, high-order numerical schemes for the generalized Korteweg—de Vries equation
• Fourth-Order Time-Stepping for Stiff PDEs
• Remarks on the Mass Constraint for KP-Type Equations
• Explicit Exponential Runge--Kutta Methods for Semilinear Parabolic Problems

This page was built for publication: Numerical study of blow-up in solutions to generalized Kadomtsev-Petviashvili equations