Biological multi-rogue waves in discrete nonlinear Schrödinger equation with saturable nonlinearities

Abstract The discrete multi-rogue waves (DMRW) as solution of the discrete nonlinear Schrodinger (DNLS) equation with saturable nonlinearities is studied numerically. These biological rogue waves represent the complex probability amplitude of finding an amide-I vibrational quantum at a site. We observe that the growth in the higher order saturable nonlinearity implies the formation of DMRW including an increase in the short-living DMRW and a decrease in amplitude of the long-living DMRW.

[1]  Alwyn C. Scott,et al.  Davydov’s Soliton , 1992 .

[2]  N. Akhmediev,et al.  Waves that appear from nowhere and disappear without a trace , 2009 .

[3]  C. Yuce,et al.  Discrete rogue waves in an array of waveguides , 2015, 2015 11th Conference on Lasers and Electro-Optics Pacific Rim (CLEO-PR).

[4]  L. Hadzievski,et al.  Bifurcation analysis of the localized modes dynamics in lattices with saturable nonlinearity , 2006 .

[5]  Fabio Baronio,et al.  Solutions of the vector nonlinear Schrödinger equations: evidence for deterministic rogue waves. , 2012, Physical review letters.

[6]  Nail Akhmediev,et al.  Rogue waves as spatial energy concentrators in arrays of nonlinear waveguides. , 2009, Optics letters.

[7]  W. Forner.  Davydov soliton dynamics: two-quantum states and diagonal disorder , 1991 .

[8]  Vladimir E. Zakharov,et al.  Modulation instability of Stokes wave → freak wave , 2005 .

[9]  D. H. Peregrine,et al.  Water waves, nonlinear Schrödinger equations and their solutions , 1983, The Journal of the Australian Mathematical Society. Series B. Applied Mathematics.

[10]  Modulational instability: first step towards energy localization in nonlinear lattices , 1997 .

[11]  A. Davydov,et al.  Solitary excitons in one‐dimensional molecular chains , 1973 .

[12]  Fajun Yu,et al.  Multi-rogue waves for a higher-order nonlinear Schrödinger equation in optical fibers , 2013, Appl. Math. Comput..

[13]  Adrian Ankiewicz,et al.  Discrete rogue waves of the Ablowitz-Ladik and Hirota equations. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Alwyn C. Scott,et al.  Launching a Davydov Soliton: II. Numerical Studies , 1984 .

[15]  Adrian Ankiewicz,et al.  Modulation instability, Fermi-Pasta-Ulam recurrence, rogue waves, nonlinear phase shift, and exact solutions of the Ablowitz-Ladik equation. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  J. Soto-Crespo,et al.  Extreme waves that appear from nowhere: On the nature of rogue waves , 2009 .

[17]  P. Kevrekidis,et al.  Multibreathers in Klein–Gordon chains with interactions beyond nearest neighbors , 2012, 1204.5496.

[18]  R. García-Salcedo,et al.  Soliton Structures in a Molecular Chain Model with Saturation , 2008, 0804.0222.

[19]  Clément Tchawoua,et al.  Multisolitons and stability of two hump solitons of upper cutoff mode in discrete electrical transmi , 2011 .

[20]  Cristina Masoller,et al.  Deterministic optical rogue waves. , 2011, Physical review letters.

[21]  B. Jalali,et al.  Optical rogue waves , 2007, Nature.

[22]  Taehoon Ahn.  Multisite oscillations in networks of weakly coupled autonomous oscillators , 1998 .

[23]  J. C. Ross,et al.  Multibreathers and homoclinic orbits in 1-dimensional nonlinear lattices , 2000 .

[24]  Panayotis G. Kevrekidis,et al.  The Discrete Nonlinear Schrödinger Equation: Mathematical Analysis, Numerical Computations and Physical Perspectives , 2009 .