Bright, dark soliton for cubic-quintic nonlinear Schrodinger

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SUMMARY

The discussion centers on the cubic-quintic nonlinear Schrödinger equation represented as EU=-U_XX+G1|U|^2U+G2|U|^4U, highlighting the existence of both bright and dark solitons. It is established that while the bright soliton solutions are accurate, numerous references contain errors regarding the dark soliton solutions. Participants seek clarification on the specific references that incorrectly present dark soliton solutions and request guidance on identifying correct solutions.

PREREQUISITES
  • Understanding of nonlinear Schrödinger equations
  • Familiarity with soliton theory
  • Knowledge of mathematical notation used in differential equations
  • Experience with cubic-quintic nonlinear dynamics
NEXT STEPS
  • Review literature on cubic-quintic nonlinear Schrödinger equations
  • Investigate the derivation of dark soliton solutions in nonlinear optics
  • Examine corrections in referenced papers regarding dark solitons
  • Explore numerical methods for solving nonlinear Schrödinger equations
USEFUL FOR

Researchers in nonlinear dynamics, physicists studying soliton behavior, and mathematicians focused on differential equations will benefit from this discussion.

dongsh2
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For a given stationary cubic-quintic nonlinear Schrödinger equation,
EU=-U_XX+G1|U|^2U+G2 |U|^4 U, where X=X(t,x). There are bright and dark solitons. In many references, it is found that there is typo or mistake in dark soliton by substituting their soliton solution to this above eqaution. The bright case is OK, but the dark soliton case is incorrect. Could you please so kind point out where or which reference we can find their correct soliton solutions

Many thanks for your kind help.
 
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Could you give a reference to a paper where the dark soliton solution is incorrect?
 

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