Home Rogue-Wave Interaction of a Nonlinear Schrödinger Model for the Alpha Helical Protein
Article
Licensed
Unlicensed Requires Authentication

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

  • Hui-Xian Jia EMAIL logo , Yu-Jun Liu and Ya-Ning Wang
Published/Copyright: November 4, 2015
Zeitschrift für Naturforschung A
From the journal Zeitschrift für Naturforschung A Volume 71 Issue 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.

References

[1] S. S. Veni and M. M. Latha, Phys. Scr. 86, 025003 (2012).10.1088/0031-8949/86/02/025003Search in Google Scholar

[2] L. Brizhik, A. Eremko, B. Piette, and W. Zakrzewski, Chem. Phys. 324, 259 (2006).10.1016/j.chemphys.2006.01.033Search in Google Scholar

[3] A. S. Davydov, J. Theor. Biol. 38, 559 (1973).10.1016/0022-5193(73)90256-7Search in Google Scholar

[4] M. J. Ablowitz and P. A. Clarkson, Cambridge, UK, Cambridge Univ. Press 1991.Search in Google Scholar

[5] N. Benes, A Kasman, and K. Young, J. Nonlin. Sci. 16, 179 (2006).10.1007/s00332-005-0709-2Search in Google Scholar

[6] I. Christov and C. I. Christov, Phys. Lett. A 372, 841 (2008).10.1016/j.physleta.2007.08.038Search in Google Scholar

[7] A. S. Davydov and N. I. Kislukha, Phys. Status Solidi. (b) 59, 465 (1973).10.1002/pssb.2220590212Search in Google Scholar

[8] M. Daniel and K. Deepamala, Phys. A 221, 241 (1995).10.1016/0378-4371(95)00243-ZSearch in Google Scholar

[9] M. Daniel and M. M. Latha, Phys. A 298, 351 (2001).10.1016/S0378-4371(01)00263-1Search in Google Scholar

[10] M. Daniel and M. M. Latha, Phys. A 240, 526 (1997).10.1016/S0378-4371(97)00041-1Search in Google Scholar

[11] A. S. Davydov, A. A. Eremko, and A. I. Segienko, Ukr. Fiz. Zh. 23, 983 (1978).Search in Google Scholar

[12] A. A. Eremko and A. I. Sergienko, Ukr. J. Phys. 25, 2013 (1980).Search in Google Scholar

[13] J. M. Hyman, D. W. McLaughlin, and A. C. Scott, Phys. D 3, 23 (1981).10.1016/0167-2789(81)90117-2Search in Google Scholar

[14] D. Hennig, Phys. Rev. B 65, 174302 (2002).10.1103/PhysRevB.65.174302Search in Google Scholar

[15] A. C. Scott, Phys. Scr. 29, 279 (1984).10.1088/0031-8949/29/3/016Search in Google Scholar

[16] M. Daniel and M. M. Latha, Phys. Lett. A 252, 92 (1999).10.1016/S0375-9601(98)00936-0Search in Google Scholar

[17] M. M. Latha and S. S. Veni, Phys. Scr. 83, 035001 (2011).10.1088/0031-8949/83/03/035001Search in Google Scholar

[18] R. X. Liu, B. Tian, Y. Jiang, and P. Wang, Commun. Nonlinear Sci. Numer. Simulat. 19, 520 (2014).Search in Google Scholar

[19] D. R. Solli, C. Ropers, P. Koonath, and B. Jalali, Nature 405, 1054 (2007).10.1038/nature06402Search in Google Scholar PubMed

[20] N. Akhmediev, V. M. Eleonskii, and N. E. Kulagin, Theor. Math. Phys. 72, 809 (1987).10.1007/BF01017105Search in Google Scholar

[21] N. Akhmediev, A. Ankiewicz, and J. M. Soto-Crespo, Phys. Rev. E 80, 026601 (2009).10.1103/PhysRevA.80.043818Search in Google Scholar

[22] A. Chabchoub, N. P. Hoffmann, and N. Akhmediev, Phys. Rev. Lett. 106, 204502 (2011).10.1103/PhysRevLett.106.204502Search in Google Scholar

[23] W. Liu, Eur. Phys. J. Plus 127, 1 (2012).10.1140/epjp/i2012-12005-3Search in Google Scholar

[24] Q. B. Wang, D. S. Li, and M. Z. Liu, Chaos Soliton. Fract. 42, 3087 (2009).10.1016/j.chaos.2009.04.008Search in Google Scholar

[25] D. W. Zuo, Y. T. Gao, X. Yu, Y. H. Sun, and L. Xue, Z. Naturforsch. A 70, 309 (2015).10.1515/zna-2014-0340Search in Google Scholar

[26] D. W. Zuo, Y. T. Gao, L. Xue, and Y. J. Feng, Chaos Solitons. Fract. 69, 217 (2014).10.1016/j.chaos.2014.09.017Search in Google Scholar

[27] H. X. Jia, J. Y. Ma, Y. J. Liu, and X. F. Liu, Ind. J. Phys. 89, 281 (2015).10.1007/s12648-014-0544-0Search in Google Scholar

[28] X. Y. Gao, Eur. Phys. Lett. 110, 15002 (2015).10.1209/0295-5075/110/15002Search in Google Scholar

[29] X. Y. Gao, J. Math. Phys. 56, 014101 (2015).10.7567/JJAP.56.014101Search in Google Scholar

[30] X. Y. Gao, Ocean Eng. 96, 245 (2015).10.1016/j.oceaneng.2014.12.017Search in Google Scholar

[31] X. Y. Gao, Z. Naturforsch. A 70, 59 (2015).10.1016/j.repl.2015.01.026Search in Google Scholar

[32] A. Hesegawa and Y. Kodama, Oxford, UK, Oxford Univ. Press 1995.Search in Google Scholar

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

©2016 by De Gruyter

Articles in the same Issue

  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
Keywords for this article
Darboux Transformation; Davydov Soliton; Higher-Order Rogue Waves

Articles in the same Issue

  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
Sign up now to receive a 20% welcome discount
Institutional Access
How does access work?
Have an idea on how to improve our website?
Please write us.
© 2025 De Gruyter Brill
Downloaded on 22.9.2025 from https://www.degruyterbrill.com/document/doi/10.1515/zna-2015-0306/html?lang=en
Scroll to top button