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Exact Elliptic Compactons in Generalized Korteweg-DeVries Equations
Fred Cooper, Avinash Khare, Avadh Saxena
We derive a general theorem relating the energy, momentum and velocity of any solitary wave solution of the generalized KdV equation which enables us to relate the amplitude, width…
Asymptotic Calculation of Discrete Nonlinear Wave Interactions
P. G. Kevrekidis, Avinash Khare, A. Saxena +2
We illustrate how to compute asymptotic interactions between discrete solitary waves of dispersive equations, using the approach proposed by Manton [Nucl. Phys. B 150, 397 (1979)].…
Quasi-Periodic Solutions of Heun's Equation
Avinash Khare, Uday Sukhatme
By exploiting a recently developed connection between Heun's differential equation and the generalized associated Lamé equation, we not only recover the well known periodic solutio…
PT-Invariant Periodic Potentials with a Finite Number of Band Gaps
Avinash Khare, Uday Sukhatme
We obtain the band edge eigenstates and the mid-band states for the complex, PT-invariant generalized associated Lamé potentials $V^{PT}(x)=-a(a+1)m \sn^2(y,m)-b(b+1)m {\sn^2 (y+K(…
Statistical Mechanics of Lamé Solitons
Ioana Bena, Avinash Khare, Avadh Saxena
We study the exact statistical mechanics of Lamé solitons using a transfer matrix method. This requires a knowledge of the first forbidden band of the corresponding Schrödinger equ…
Exact solitary wave solutions for a discrete field theory in 1+1 dimensions
Fred Cooper, Avinash Khare, Bogdan Mihaila +1
We have found exact, periodic, time-dependent solitary wave solutions of a discrete field theory model. For finite lattices, depending on whether one is considering a repulsi…