An easy to implement modulus-squared Dirichlet (MSD) boundary condition is formulated for numerical simulations of time-dependent complex partial differential equations in multidimensional settings. The MSD boundary condition approximates a constant modulus-squared value of the solution at the boundaries and is defined as ∂Ψ ∂t |b ≈ i Im[ 1 Ψb−1 ∂Ψ ∂t |b−1] Ψb, where Ψ is the complex field and ...

The nonlinear reflection curve due to a van der Pol type boundary condition at the right end becomes a multivalued relation when one of the parameters (α) exceeds the characteristic impedance value (α = 1). From stability and continuity considerations, we prescribe kinematic admissibility and define hysteresis iterations with memory effects, whose dynamical behavior is herein investigated. Assu...

   The present article describes the effects of thermal radiation and heat source/sink parameters on the mixed convective magnetohydrodynamic flow of a Casson nanofluid with zero normal flux of nanoparticles over an exponentially stretching sheet along with convective boundary condition. The governing nonlinear system of partial differential equations along with boundary conditions...

In the boundary layers around the edges of images, basic nonlinear parabolic equations for image intensity used in image processing assume a special degenerate asymptotic form. An asymptotic self-similar solution to this degenerate equation is obtained in an explicit form. The solution reveals a substantially nonlinear effect-the formation of sharp steps at the edges of the images, leading to e...

We consider the initial boundary value (IBV) problem for focusing nonlinear Schrodinger equation in quarter plane x>0, t >0 case of periodic data, u(x,0) = ? exp(?2i?x) (or asymptotically periodic, u(x, 0) =? exp(?2i?x)?0 as x??), and a Robin condition at x 0: ux(0, t)+qu(0, t) 0, q ? 0. Our approach is based on unified transform (the Fokas method) combined with symmetry considerations correspo...