×

zbMATH — the first resource for mathematics

Chiral nonlinear Schrödinger equation. (English) Zbl 0932.35190
Summary: A nonlinear evolution equation \[ i\psi_t+ \psi_{xx}- i\lambda(\psi^*\psi_x- \psi\psi^*_x)\psi= 0, \] which we name the chiral nonlinear Schrödinger (CNLS) equation is studied. The CNLS equation has two kinds of progressive wave solutions; bright soliton for \(\lambda v>0\) and dark soliton for \(\lambda v<0\), where \(v\) is the velocity of the envelope. The bright soliton corresponds to the particle while the dark soliton is interpreted as the hole.

MSC:
35Q55 NLS equations (nonlinear Schrödinger equations)
37K40 Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems
PDF BibTeX Cite
Full Text: DOI
References:
[1] Aglietti, U.; Griguolo, L.; Jackiw, R.; Pi, S.Y.; Semirara, D., Anyons and chiral solitons on a line, Phys. rev. lett., 77, 4406-4409, (1996)
[2] Mio, K.; Ogino, T.; Minami, K.; Takeda, S.; Mio, K.; Ogino, T.; Minami, K.; Takeda, S., Modified nonlinear Schrödinger equation for alfven waves propagating along the magnetic field in cold plasmas, J. phys. soc. jpn., J. phys. soc. jpn., 41, 271, (1976) · Zbl 1334.76181
[3] Wadati, M.; Sanuki, H.; Konno, K.; Ichikawa, Y.H.; Wadati, M.; Sanuki, H.; Konno, K.; Ichikawa, Y.H., Circular polarized nonlinear alfven waves, Rocky mountain math. journal, Rocky mountain math. journal, 8, 331, (1978) · Zbl 0391.76090
[4] Wadati, M.; Sanuki, H.; Konno, K.; Ichikawa, Y.H., Proc. of the conference on theory and application of soliton, (Jan. 5-10 1976), Tucson, Arizona
[5] Ichikawa, Y.; Konno, K.; Wadati, M.; Sanuki, H.; Ichikawa, Y.; Konno, K.; Wadati, M.; Sanuki, H., Spiky soliton in circular polarized alfven wave, J. phys. soc. jpn., J. phys. soc. jpn., 48, 286, (1980)
[6] Kaup, D.J.; Newell, A.C.; Kaup, D.J.; Newell, A.C., An exact soliton for a derivative nonlinear Schrödinger equation, J. math. phys., J. math. phys., 19, 801, (1978) · Zbl 0383.35015
[7] Wadati, M.; Sogo, K.; Wadati, M.; Sogo, K., Gauge transformations in soliton theory, J. phys. soc. jpn., J. phys. soc. jpn., 52, 398, (1983)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.