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197 papers
Hyperbolic, Trigonometric and Periodic Solutions of Local and Nonlocal Fokas-Lennels Equations
Avinash Khare, Avadh Saxena
We obtain a large number of exact hyperbolic, trigonometric, and periodic solutions in terms of Jacobi elliptic functions as well as algebraic solutions with a power law tail of th…
Two-Parameter Family of Nonlinear Dirac Equations With Scalar-Scalar plus Vector-Vector Interactions
Avinash Khare, Fred Cooper, John F. Dawson +1
We obtain exact solutions of the nonlinear Dirac equation in dimensions of the form for scalar-scalar (SS) plus vector-vector (VV) interaction with i…
Linear Superposition of Quadratic Functions in a Fifth Order KdV-Type Equation
Avinash Khare, Avadh Saxena
We show that a fifth order KdV-type equation admits several real as well as complex parity-time reversal or PT-invariant solutions with linear superposition of quadratic functions…
Some Novel Aspects of the Plane Pendulum in Classical Mechanics
Avinash Khare, Avadh Saxena
We obtain a novel connection between the exact solutions of the plane pendulum, hyperbolic plane pendulum and inverted plane pendulum equations as well as the static solutions of t…
Solitons of the Symmetric -- Triple Well Model
Avinash Khare, Avadh Saxena
A symmetric -- model has recently attracted a lot of attention due to its usefulness in studying tunable phase transitions. We analyze the behavior of this model…
Solitary waves in the complementary generalized ABS model
Avinash Khare, Fred Cooper, John F. Dawson +1
We obtain exact solutions of the nonlinear Dirac equation in 1+1 dimension of the form $ Ψ(x,t) =Φ(x) \rme^{-\rmi ωt}$ where the nonlinear interactions are a combination of vector-…