# Numerical Study of Blow up and Stability of Solutions of Generalized Kadomtsev–Petviashvili Equations

@article{Klein2012NumericalSO, title={Numerical Study of Blow up and Stability of Solutions of Generalized Kadomtsev–Petviashvili Equations}, author={Christian Klein and Jean-Claude Saut}, journal={Journal of Nonlinear Science}, year={2012}, volume={22}, pages={763-811} }

We first review the known mathematical results concerning the Kadomtsev–Petviashvili type equations. Then we perform numerical simulations to analyze various qualitative properties of the equations: blow-up versus long time behavior, stability and instability of solitary waves.

## 64 Citations

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

- Mathematics
- 2013

We present a numerical study of solutions to the generalized Kadomtsev-Petviashvili equations with critical and supercritical nonlinearity for localized initial data with a single minimum and single…

### Blow-up of solutions of non-linear equations of Kadomtsev–Petviashvili and Zakharov–Kuznetsov types

- Mathematics
- 2014

The Kadomtsev–Petviashvili equation and Zakharov–Kuznetsov equation are important in physical applications. We obtain sufficient conditions for finite-time blow-up of solutions of these equations in…

### Stability of Solitary Waves of the Kadomtsev-Petviashvili Equation with a Weak Rotation

- Mathematics, PhysicsSIAM J. Math. Anal.
- 2017

In spite of the absence of any scaling invariance property for the RGKP equation, it is proved that the strong instability of the solitary waves is proved.

### Numerical Study of Blowup in the Davey-Stewartson System

- Mathematics
- 2011

Nonlinear dispersive partial differential equations such as the nonlinear Schr\"odinger equations can have solutions that blow-up. We numerically study the long time behavior and potential blowup of…

### Numerical study of the regularizing effect of the 3D weakly transverse BBM equations for long times

- MathematicsAppl. Math. Comput.
- 2013

### The Cauchy Problem for the Fractional Kadomtsev-Petviashvili Equations

- MathematicsSIAM J. Math. Anal.
- 2018

The aim of this paper is to prove various ill-posedness and well-posedness results on the Cauchy problem associated to a class of fractional Kadomtsev--Petviashvili (KP) equations, including the KP...

### On the Well-Posedness of the Dissipative Kadomtsev–Petviashvili Equation

- Mathematics
- 2020

The well-posedness of the initial-value problem associated with the dissipative Kadomtsev–Petviashvili equation in the case of two-dimensional space is studied. It is proved by using a dyadic…

### Transverse stability of periodic traveling waves in Kadomtsev-Petviashvili equations: A numerical study

- Physics, Mathematics
- 2011

We numerically investigate transverse stability and instability of so-called cnoidal waves, i.e., periodic traveling wave solutions of the Korteweg-de Vries equation, under the time-evolution of the…

### Traveling waves and transverse instability for the fractional Kadomtsev–Petviashvili equation

- Mathematics, PhysicsStudies in Applied Mathematics
- 2022

Of concern are traveling wave solutions for the fractional Kadomtsev–Petviashvili (fKP) equation. The existence of periodically modulated solitary wave solutions is proved by dimension‐breaking…

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