R el a tivis tic a n d p s e u d o r el a tivis tic fo r m ul a tio n of n o nli n e a r e n v elo p e e q u a tio n s wi t h s p a tio t e m p o r al di s p e r sio n. II. S a t u r a bl e sy s t e m s C h ri s ti a n, JM, M cDo n al d, GS, Lu n di e, MJ a n d Kots a m p a s e ri s, A h t t p:// dx. d oi.o r g/ 1 0. 1 1 0 3/P hy sR evA.9 8. 0 5 3 8 4 3 Ti t l e R el a tivis tic a n d p s e u d o r el a tivis tic fo r m ul a tio n of n o nli n e a r e nv elo p e e q u a tio n s wi t h s p a tio t e m p o r al di s p e r sio n. II.
We present, to the best of our knowledge, the first exact dark spatial solitons of a nonlinear Helmholtz equation with a self-defocusing saturable refractive-index model. These solutions capture oblique (arbitrary-angle) propagation in both the forward and backward directions, and they can also exhibit a bistability characteristic. A detailed derivation is presented, obtained by combining coordinate transformations and directintegration methods, and the corresponding solutions of paraxial theory are recovered asymptotically as a subset. Simulations examine the robustness of the new Helmholtz solitons, with stationary states emerging from a range of perturbed input beams.
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