506 research outputs found
Two-soliton solution for the derivative nonlinear Schr\"odinger equation with nonvanishing boundary conditions
An explicit two-soliton solution for the derivative nonlinear Schr\"odinger
equation with nonvanishing boundary conditions is derived, demonstrating
details of interactions between two bright solitons, two dark solitons, as well
as one bright soliton and one dark soliton. Shifts of soliton positions due to
collisions are analytically obtained, which are irrespective of the bright or
dark characters of the participating solitons.Comment: 11 pages, 4 figures. Phys. Lett. A 2006 (in press
Directional Soliton and Breather Beams
Solitons and breathers are nonlinear modes that exist in a wide range of
physical systems. They are fundamental solutions of a number of nonlinear wave
evolution equations, including the uni-directional nonlinear Schr\"odinger
equation (NLSE). We report the observation of slanted solitons and breathers
propagating at an angle with respect to the direction of propagation of the
wave field. As the coherence is diagonal, the scale in the crest direction
becomes finite, consequently, a beam dynamics forms. Spatio-temporal
measurements of the water surface elevation are obtained by
stereo-reconstructing the positions of the floating markers placed on a regular
lattice and recorded with two synchronized high-speed cameras. Experimental
results, based on the predictions obtained from the (2D+1) hyperbolic NLSE
equation, are in excellent agreement with the theory. Our study proves the
existence of such unique and coherent wave packets and has serious implications
for practical applications in optical sciences and physical oceanography.
Moreover, unstable wave fields in this geometry may explain the formation of
directional large amplitude rogue waves with a finite crest length within a
wide range of nonlinear dispersive media, such as Bose-Einstein condensates,
plasma, hydrodynamics and optics
Exploring the Dynamics of Nonlocal Nonlinear Waves: Analytical Insights into the Extended Kadomtsev-Petviashvili Model
The study of nonlocal nonlinear systems and their dynamics is a rapidly
increasing field of research. In this study, we take a closer look at the
extended nonlocal Kadomtsev-Petviashvili (enKP) model through a systematic
analysis of explicit solutions. Using a superposed bilinearization approach, we
obtained a bilinear form of the enKP equation and constructed soliton
solutions. Our findings show that the nature of the resulting nonlinear waves,
including the amplitude, width, localization, and velocity, can be controlled
by arbitrary solution parameters. The solutions exhibited both symmetric and
asymmetric characteristics, including localized bell-type bright solitons,
superposed kink-bell-type and antikink-bell-type soliton profiles. The solitons
arising in this nonlocal model only undergo elastic interactions while
maintaining their initial identities and shifting phases. Additionally, we
demonstrated the possibility of generating bound-soliton molecules and
breathers with appropriately chosen soliton parameters. The results of this
study offer valuable insights into the dynamics of localized nonlinear waves in
higher-dimensional nonlocal nonlinear models.Comment: 22 pages, 10 figures; submitted to journa
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