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Rogue-Wave Interaction of a Nonlinear Schrödinger Model for the Alpha Helical Protein

  • Hui-Xian Jia EMAIL logo , Yu-Jun Liu und Ya-Ning Wang
Veröffentlicht/Copyright: 4. November 2015
Zeitschrift für Naturforschung A
Aus der Zeitschrift Zeitschrift für Naturforschung A Band 71 Heft 1

Abstract

In this article, we investigate a fourth-order nonlinear Schrödinger equation, which governs the Davydov solitons in the alpha helical protein with higher-order effects. By virtue of the generalised Darboux transformation, higher-order rogue-wave solutions are derived. Propagation and interaction of the rogue waves are analysed: (i) Coefficients affect the existence time of the first-order rogue waves; (ii) coefficients affect the interaction time of the second- and third-order rogue waves; (iii) direction of the rogue-wave propagation remain unchanged after interaction.

Keywords: Darboux Transformation; Davydov Soliton; Higher-Order Rogue Waves
PACS numbers:: 47.35.Fg; 05.45.Yv; 02.30.Jr
Corresponding author: Hui-Xian Jia, Department of Basic, Shijiazhuang Post and Telecommunication Technical College, Shijiazhuang 050021, China, E-mail:

Acknowledgments

We express our sincere thanks to all the members of our discussion group for their valuable comments. This work has been supported by the Foundation of Hebei Education Department of China under Grant No. QN2015051.

Appendix A

θ^^1[2] = 1480(45ieit2 − 210eit2t − 28140eit2rt − 1080ieit2t2 − 28320ieit2rt2 − 131040ieit2r2t2 +1200eit2t3 + 36960eit2rt3 + 313920eit2r2t3 + 812160eit2r3t3 + 80ieit2t4 + 1920ieit2rt4 + 17280ieit2r2t4 +69120ieit2r3t4 + 103680ieit2r4t4 − 32eit2t5 − 960eit2rt5 − 11520eit2r2t5 − 69120eit2r3t5 − 207360eit2r4t5 −248832eit2r5t5 + 30ieit2x + 1200eit2tx + 22560eit2rtx + 2640ieit2t2x + 62400ieit2rt2x + 279360ieit2r2t2x −320eit2t3x − 5760eit2rt3x − 34560eit2r2t3x − 69120eit2r3t3x − 160ieit2t4x − 3840ieit2rt4x − 34560ieit2r2t4x−138240ieit2r3t4x − 207360ieit2r4t4x + 120ieit2x2 − 1680eit2tx2 − 25440eit2rtx2 − 480ieit2t2x2 − 5760ieit2rt2x2−17280ieit2r2t2x2 + 320eit2t3x2 + 5760eit2rt3x2 + 34560eit2r2t3x2 + 69120eit2r3t3x2 − 240ieit2x3 + 320eit2tx3+1920eit2rtx3 + 320ieit2t2x3 + 3840ieit2rt2x3 + 11520ieit2r2t2x3 + 80ieit2x4 − 160eit2tx4 − 960eit2rtx4 −32ieit2x5),

θ^1[2] = 1480e−  it2(−45 + 210it + 28140irt + 1080t2 + 28320rt2 + 131040r2t2 − 1200it3 − 36960irt3 −313920ir2t3 − 812160ir3t3 − 80t4 − 1920rt4 − 17280r2t4 − 69120r3t4 − 103680r4t4 + 32it5 + 960irt5 +11520ir2t5 + 69120ir3t5 + 207360ir4t5 + 248832ir5t5 + 30x + 1200itx + 22560irtx + 2640t2x +62400rt2x + 279360r2t2x − 320it3x − 5760irt3x − 34560ir2t3x − 69120ir3t3x − 160t4x − 3840rt4x −34560r2t4x − 138240r3t4x − 207360r4t4x − 120x2 + 1680itx2 + 25440irtx2 + 480t2x2 + 5760rt2x2 +17280r2t2x2 − 320it3x2 − 5760irt3x2 − 34560ir2t3x2 − 69120ir3t3x2 − 240x3 + 320itx3 + 1920irtx3 +320t2x3 + 3840rt2x3 + 11520r2t2x3 − 80x4 + 160itx4 + 960irtx4 − 32x5).

Appendix B

q^^[2] = 45 + 360it + 4464irt − 468t2 − 7920rt2 + 6192r2t2 − 192it3 − 12672irt3 − 131328ir2t3 −373248ir3t3 − 528t4 − 9600rt4 − 58752r2t4 − 124416r3t4 − 20736r4t4 − 384it5 − 11520irt5 −138240ir2t5 − 829440ir3t5 − 2488320ir4t5 − 2985984ir5t5 + 64t6 + 2304rt6 + 34560r2t6 + 276480r3t6 +1244160r4t6 + 2985984r5t6 + 2985984r6t6 − 180x2 + 576itx2 + 12672irtx2 − 1440t2x2 − 26496rt2x2 −107136r2t2x2 − 768it3x2 − 13824irt3x2 − 82944ir2t3x2 − 165888ir3t3x2 + 192t4x2 + 4608rt4x2+41472r2t4x2 + 165888r3t4x2 + 248832r4t4x2 − 144x4 − 384itx4 − 2304irtx4 + 192t2x4 + 2304rt2x4 +6912r2t2x4 + 64x6,

q^[2] = 9 + 396t2 + 11664rt2 + 92592r2t2 + 432t4 + 13440rt4 + 148608r2t4 + 705024r3t4 +1223424r4t4 + 64t6 + 2304rt6 + 34560r2t6 + 276480r3t6 + 1244160r4t6 + 2985984r5t6 + 2985984r6t6 +108x2 − 288t2x2 − 12672rt2x2 − 65664r2t2x2 + 192t4x2 + 4608rt4x2 + 41472r2t4x2 + 165888r3t4x2 +248832r4t4x2 + 48x4 + 192t2x4 + 2304rt2x4 + 6912r2t2x4 + 64x6.

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Received: 2015-7-9
Accepted: 2015-10-9
Published Online: 2015-11-4
Published in Print: 2016-1-1

©2016 by De Gruyter

Artikel in diesem Heft

  1. Frontmatter
  2. Theoretical Investigations on the Elastic and Thermodynamic Properties of Rhenium Phosphide
  3. Lax Pair, Conservation Laws, Solitons, and Rogue Waves for a Generalised Nonlinear Schrödinger–Maxwell–Bloch System under the Nonlinear Tunneling Effect for an Inhomogeneous Erbium-Doped Silica Fibre
  4. Effect of Trace Fe3+ on Luminescent Properties of CaWO4: Pr3+ Phosphors
  5. Rogue-Wave Interaction of a Nonlinear Schrödinger Model for the Alpha Helical Protein
  6. Multi-Scale Long-Range Magnitude and Sign Correlations in Vertical Upward Oil–Gas–Water Three-Phase Flow
  7. Theoretical Study of Geometries, Stabilities, and Electronic Properties of Cationic (FeS)n+ (n = 1–5) Clusters
  8. Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation
  9. Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential
  10. Solitons, Bäcklund Transformation, Lax Pair, and Infinitely Many Conservation Law for a (2+1)-Dimensional Generalised Variable-Coefficient Shallow Water Wave Equation
  11. The Non-Alignment Stagnation-Point Flow Towards a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Buongiorno’s Model: A Revised Model
  12. Rapid Communication
  13. Extrinsic and Intrinsic Contributions to Plasmon Peaks in Solids
https://doi.org/10.1515/zna-2015-0306
Schlagwörter für diesen Artikel
Darboux Transformation; Davydov Soliton; Higher-Order Rogue Waves

Artikel in diesem Heft

  1. Frontmatter
  2. Theoretical Investigations on the Elastic and Thermodynamic Properties of Rhenium Phosphide
  3. Lax Pair, Conservation Laws, Solitons, and Rogue Waves for a Generalised Nonlinear Schrödinger–Maxwell–Bloch System under the Nonlinear Tunneling Effect for an Inhomogeneous Erbium-Doped Silica Fibre
  4. Effect of Trace Fe3+ on Luminescent Properties of CaWO4: Pr3+ Phosphors
  5. Rogue-Wave Interaction of a Nonlinear Schrödinger Model for the Alpha Helical Protein
  6. Multi-Scale Long-Range Magnitude and Sign Correlations in Vertical Upward Oil–Gas–Water Three-Phase Flow
  7. Theoretical Study of Geometries, Stabilities, and Electronic Properties of Cationic (FeS)n+ (n = 1–5) Clusters
  8. Explanation of the Quantum-Mechanical Particle-Wave Duality through the Emission of Watt-Less Gravitational Waves by the Dirac Equation
  9. Closed Analytical Solutions of the D-Dimensional Schrödinger Equation with Deformed Woods–Saxon Potential Plus Double Ring-Shaped Potential
  10. Solitons, Bäcklund Transformation, Lax Pair, and Infinitely Many Conservation Law for a (2+1)-Dimensional Generalised Variable-Coefficient Shallow Water Wave Equation
  11. The Non-Alignment Stagnation-Point Flow Towards a Permeable Stretching/Shrinking Sheet in a Nanofluid Using Buongiorno’s Model: A Revised Model
  12. Rapid Communication
  13. Extrinsic and Intrinsic Contributions to Plasmon Peaks in Solids
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