191 citations · 542 across the 7 of their papers we have counts for
7 papers
Interactions and Asymptotics of Dispersive Shock Waves -- Korteweg-de Vries Equation
Mark J. Ablowitz, Douglas E. Baldwin
The long-time asymptotic solution of the Korteweg-de Vries equation for general, step-like initial data is analyzed. Each sub-step in well-separated, multi-step data forms its own…
Nonlinear shallow ocean wave soliton interactions on flat beaches
Mark J. Ablowitz, Douglas E. Baldwin
Ocean waves are complex and often turbulent. While most ocean wave interactions are essentially linear, sometimes two or more waves interact in a nonlinear way. For example, two or…
A Symbolic Algorithm for Computing Recursion Operators of Nonlinear PDEs
D. E. Baldwin, W. Hereman
A recursion operator is an integro-differential operator which maps a generalized symmetry of a nonlinear PDE to a new symmetry. Therefore, the existence of a recursion operator gu…
Soliton Generation and Multiple Phases in Dispersive Shock and Rarefaction Wave Interaction
M. J. Ablowitz, D. E. Baldwin, M. A. Hoefer
Interactions of dispersive shock (DSWs) and rarefaction waves (RWs) associated with the Korteweg-de Vries equation are shown to exhibit multiphase dynamics and isolated solitons. T…
Symbolic Software for the Painleve Test of Nonlinear Ordinary and Partial Differential Equations
Douglas Baldwin, Willy Hereman
The automation of the traditional Painleve test in Mathematica is discussed. The package PainleveTest.m allows for the testing of polynomial systems of ordinary and partial differe…
Symbolic computation of hyperbolic tangent solutions for nonlinear differential-difference equations
Douglas Baldwin, Unal Goktas, Willy Hereman
A new algorithm is presented to find exact traveling wave solutions of differential-difference equations in terms of tanh functions. For systems with parameters, the algorithm dete…