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Nonautonomous bright soliton solutions on continuous wave and cnoidal wave backgrounds in blood vessels

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Abstract

We discuss the dissipative nonlinear Schrödinger equation (NLSE) with a variable coefficient in blood vessels via a NLSE-based constructive method and obtain exact nonautonomous soliton solutions including bright soliton solutions on continuous wave (cw) and cnoidal wave (cnw) backgrounds. Moreover, the dynamical behaviors of these soliton solutions are studied. The impact of the cw background on the separating and interactive soliton behaviors is investigated. These behaviors of the soliton can be modulated by adjusting the amplitude of background wave. The propagation behaviors of solitons on the cnw background in different dispersion systems are also studied. These results are potentially useful for future experiments in various blood vessels.

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References

  1. Zhong, W.P., Belić, M.R., Huang, T.W.: Two-dimensional accessible solitons in PT-symmetric potentials. Nonlinear Dyn. 70, 2027–2034 (2012)

    Article  Google Scholar 

  2. Biswas, A., Khalique, C.M.: Stationary solutions for non-linear dispersive Schrödinger’s equation. Nonlinear Dyn. 63, 623–626 (2011)

    Article  MathSciNet  Google Scholar 

  3. Zhu, H.P.: Nonlinear tunneling for controllable rogue waves in two dimensional graded-index waveguides. Nonlinear Dyn. 72, 873–882 (2013)

    Article  Google Scholar 

  4. Demiray, H.: Nonlinear wave modulation in a fluid-filled elastic tube with stenosis. Z. Naturforsch. A 63, 24–34 (2008)

    Google Scholar 

  5. Wu, X.F., Hua, G.S., Ma, Z.Y.: Evolution of optical solitary waves in a generalized nonlinear Schrodinger equation with variable coefficients. Nonlinear Dyn. 70, 2259–2267 (2012)

    Article  MathSciNet  Google Scholar 

  6. Belyaeva, T.L., Serkin, V.N.: Nonautonomous solitons: applications from nonlinear optics to BEC and hydrodynamics. In: Schulz, H. (ed.) Hydrodynamics—Advanced Topics (2011). Chap. 3

    Google Scholar 

  7. Serkin, V.N., Hasegawa, A., Belyaeva, T.L.: Solitary waves in nonautonomous nonlinear and dispersive systems: nonautonomous solitons. J. Mod. Opt. 57, 1456–1472 (2010)

    Article  MATH  Google Scholar 

  8. Serkin, V.N., Hasegawa, A., Belyaeva, T.L.: Nonautonomous solitons in external potentials. Phys. Rev. Lett. 98, 074102 (2007)

    Article  Google Scholar 

  9. Yomosa, S.: Solitary waves in large blood vessels. J. Phys. Soc. Jpn. 56, 506–520 (1987)

    Article  MathSciNet  Google Scholar 

  10. Duan, W.S., Wang, B.R.: Reflection and transmission of nonlinear blood waves due to arterial branching. Phys. Rev. E 55, 1773–1778 (1997)

    Article  Google Scholar 

  11. Misra, J.C., Patra, M.K.: A study of solitary waves in a tapered aorta by using the theory of solitons. Comput. Math. Appl. 54, 242–254 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  12. Demiray, H.: Modulation of non-linear waves in a viscous fluid contained in an elastic tube. Int. J. Non-Linear Mech. 36, 649–661 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  13. Tay, K.G., Choy, Y.Y., Ong, C.T., Demiray, H.: Dissipative nonlinear Schrodinger equation with variable coefficient in a stenosed elastic tube filled with a viscous fluid. Int. J. Eng. Sci. Technol. 2, 708–723 (2010)

    Google Scholar 

  14. Demiray, H.: Nonlinear waves in a viscous fluid contained in an elastic tube with variable cross-section. Int. J. Non-Linear Mech. 41, 258–270 (2006)

    Article  Google Scholar 

  15. Xu, T., Zhang, C.Y., Wei, G.M., Li, J., Meng, X.H., Tian, B.: Symbolic-computation construction of transformations for a more generalized nonlinear Schrodinger equation with applications in inhomogeneous plasmas, optical fibers, viscous fluids and Bose–Einstein condensates. Eur. Phys. J. B 55, 323–332 (2007)

    Article  Google Scholar 

  16. Choy, Y.Y., Tay, K.G., Ong, C.T.: NLS equation with variable coefficient in a stenosed elastic tube filled with an averaged inviscid fluid. World Appl. Sci. J. 16, 622–631 (2012)

    Google Scholar 

  17. Choy, Y.Y., Tay, K.G., Ong, C.T.: Nonlinear waves in fluid-filled stenosed elastic tube: nonlinear Schrodinger equation with variable coefficient. World Acad. Sci., Eng. Technol. 56, 105–108 (2011)

    Google Scholar 

  18. Zhao, L.H., Wang, Y.Y., Dai, C.Q.: Solitons and their interactions in a tapered aorta. Phys. Scr. 84, 065401 (2011)

    Article  Google Scholar 

  19. Dai, C.Q., Zhang, J.F.: Controllable dynamical behaviors for spatiotemporal bright solitons on continuous wave background. Nonlinear Dyn. 73, 2049–2057 (2013)

    Article  MathSciNet  Google Scholar 

  20. Bélanger, N., Bélanger, P.A.: Bright solitons on a cw background. Opt. Commun. 124, 301–308 (1996)

    Article  Google Scholar 

  21. Shin, H.J.: Soliton scattering from a finite cnoidal wave train in a fiber. Phys. Rev. E 63, 026606 (2001)

    Article  Google Scholar 

  22. Lü, Z.S.: A Burgers equation-based constructive method for solving nonlinear evolution equations. Phys. Lett. A 353, 158–160 (2006)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgements

This work was supported by the Scientific Research Fund of Zhejiang Provincial Education Department (Grant No. Y201225803), the National Natural Science Foundation of China (Grant No. 11375007), the Zhejiang Provincial Natural Science Foundation of China (Grant No. LY13F050006), the Zhejiang Province Undergraduate Scientific and Technological Innovation Project (Grant No. 2013R412034), the Student Research Training Program (Grant No. 201212007), and Undergraduate Innovative Base of Zhejiang A&F University.

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  1. School of Sciences, Zhejiang A&F University, Lin’an, Zhejiang, 311300, P.R. China

    Hua-Jie Jiang, Jia-Jie **ang, Chao-Qing Dai & Yue-Yue Wang

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  1. Hua-Jie Jiang
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  2. Jia-Jie **ang
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  4. Yue-Yue Wang
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Correspondence to Chao-Qing Dai.

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Jiang, HJ., **ang, JJ., Dai, CQ. et al. Nonautonomous bright soliton solutions on continuous wave and cnoidal wave backgrounds in blood vessels. Nonlinear Dyn 75, 201–207 (2014). https://doi.org/10.1007/s11071-013-1058-6

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