Properties of soliton-soliton collisions

Aossey, David W.; Skinner, Steven R.; Cooney, J.; Williams, J. E.; Gavin, Matthew T.; Andersen, David R.; Lonngren, Karl E.

doi:10.1103/physreva.45.2606

Cited by 34 publications

(16 citation statements)

References 10 publications

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“…Aossey et al [38] compared their results for the ratio of the phase shifts as a function of the ratio of the amplitudes for the KdV solitons, with those obtained in the experiments of Ikezi, Taylor, and Baker [42], and those obtained from numerical work of Zabusky and Kruskal [31] and Lamb [41], as shown in Fig. 4(b).…”

Section: Mechanism and Rules Of Collision Of The Microscopic Particlementioning

confidence: 87%

“…3(a). In this case, Aossey et al [38] considered two MIPs with different amplitudes. The details of what occurs during the collision need not concern us here other than to note that the MIPs with the larger-amplitude has completely passed through the one with the smaller amplitude.…”

Section: Mechanism and Rules Of Collision Of The Microscopic Particlementioning

confidence: 98%

“…The properties and rules of such collision between two microscopic particles have been first studied by Aossey et al [38]. Both the phase shift of the microscopic particles after their interaction and the range of the interaction are functions of the relative amplitude of the two colliding microscopic particles.…”

Section: Mechanism and Rules Of Collision Of The Microscopic Particlementioning

confidence: 99%

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Features and states of microscopic particles in nonlinear quantum-mechanics systems

Pang

2008

Front. Phys. China

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In this paper, we present the elementary principles of nonlinear quantum mechanics (NLQM), which is based on some problems in quantum mechanics. We investigate in detail the motion laws and some main properties of microscopic particles in nonlinear quantum systems using these elementary principles. Concretely speaking, we study in this paper the wave-particle duality of the solution of the nonlinear Schrödinger equation, the stability of microscopic particles described by NLQM, invariances and conservation laws of motion of particles, the Hamiltonian principle of particle motion and corresponding Lagrangian and Hamilton equations, the classical rule of microscopic particle motion, the mechanism and rules of particle collision, the features of reflection and the transmission of particles at interfaces, and the uncertainty relation of particle motion as well as the eigenvalue and eigenequations of particles, and so on. We obtained the invariance and conservation laws of mass, energy and momentum and angular momentum for the microscopic particles, which are also some elementary and universal laws of matter in the NLQM and give further the methods and ways of solving the above questions. We also find that the laws of motion of microscopic particles in such a case are completely different from that in the linear quantum mechanics (LQM). They have a lot of new properties; for example, the particles possess the real wave-corpuscle duality, obey the classical rule of motion and conservation laws of energy, momentum and mass, satisfy minimum uncertainty relation, can be localized due to the nonlinear interaction, and its position and momentum can also be determined, etc. From these studies, we see clearly that rules and features of microscopic particle motion in NLQM is different from that in LQM. Therefore, the NLQM is a new physical theory, and a necessary result of the development of quantum mechanics and has a correct representation of describing microscopic particles in nonlinear systems, which can solve problems disputed for about a century by scientists in the LQM field. Hence, the NLQM built is very necessary and correct. The NLQM established can promote the development of physics and can enhance and raise the knowledge and recognition levels to the essences of microscopic matter. We can predict that nonlinear quantum mechanics has extensive applications in physics, chemistry, biology and polymers, etc. 02 .60.Cb, As is known, the quantum mechanics established by several great scientists such as Bohr, Born, Schrödinger and Heisenberg, etc., in the early 1900s [1 − 6] is the science describing the properties and rules of motion of microscopic particles (MIP). It is a foundation of modern science, in which the state of microscopic particles is described by the Schrödinger equation: PACS numberswhere 2 ∇ 2 /2m is the kinetic energy operator, V (r, t) is

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Section: Mechanism and Rules Of Collision Of The Microscopic Particlementioning

confidence: 87%

Section: Mechanism and Rules Of Collision Of The Microscopic Particlementioning

confidence: 98%

Section: Mechanism and Rules Of Collision Of The Microscopic Particlementioning

confidence: 99%

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Features and states of microscopic particles in nonlinear quantum-mechanics systems

Pang

2008

Front. Phys. China

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“…That is, faster solitons are "taller" and narrower than slower ones. In addition, solitons are preserved in collisions, and unlike collisions between linear pulses, an overtaking collision between two KdV solitons produces a phase shift 16 such that the overtaken ͑smaller͒ soliton is shifted backward in space while the overtaking ͑larger͒ soliton is shifted forward.…”

Section: Introductionmentioning

confidence: 99%

Experimental study of nonlinear solitary waves in two-dimensional dusty plasma

2008

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The excitation and propagation of solitary waves is studied experimentally in a two-dimensional strongly coupled dusty ͑complex͒ plasma. A single layer with Ϸ5000 microspheres ͑8 m diam͒ was suspended in an argon plasma with a neutral gas pressure of 3.0 mTorr. The measured Debye shielding parameter was Ϸ 1.6, where = a / is the ratio of the lattice constant a to the Debye length. Nonlinear, planar longitudinal waves were launched by pushing all the particles in a rectangular region at the center of the crystal in the same direction using an 18 W green laser. Compressive solitary waves with density perturbations ␦n / n 0 Շ 0.8 and widths Շ5a were found to propagate in the forward direction at speeds exceeding the dust acoustic speed. For small amplitude solitary waves, the relations between amplitude, width, and velocity are consistent with those predicted for Korteweg-deVries solitons. Rarefactive perturbations were not observed to evolve into solitary waves. However, oscillatory shocks were seen to move in the backward direction after the laser force was removed.

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“…Next we proceed with the analysis of soliton collisions using our iterative nonlinear beam propagation method and the WDF. Collision of two spatial solitons has been solved analytically using the nonlinear Schrödinger equation [2,24,25]; however, it does not give an intuitive picture of how the energy exchanges during the collision. Here, without loss of generality, we take two solitons with the same peak amplitude and no initial phase difference as the input to a Kerr nonlinear medium.…”

Section: Soliton Collisionmentioning

confidence: 99%

Hamiltonian and phase-space representation of spatial solitons

Gao¹,

Tian²,

Barbastathis³

2014

Optics Communications

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We use Hamiltonian ray tracing and phase-space representation to describe the propagation of a single spatial soliton and soliton collisions in a Kerr nonlinear medium. Hamiltonian ray tracing is applied using the iterative nonlinear beam propagation method, which allows taking both wave effects and Kerr nonlinearity into consideration. Energy evolution within a single spatial soliton and the exchange of energy when two solitons collide are interpreted intuitively by ray trajectories and geometrical shearing of the Wigner distribution functions.

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Properties of soliton-soliton collisions

Cited by 34 publications

References 10 publications

Features and states of microscopic particles in nonlinear quantum-mechanics systems

Features and states of microscopic particles in nonlinear quantum-mechanics systems

Experimental study of nonlinear solitary waves in two-dimensional dusty plasma

Hamiltonian and phase-space representation of spatial solitons

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