We analytically give the financial rogue waves in nonlinear option pricing model due to Ivancevic, which is wave alternative of Black—Scholes model. These solutions may he used describe possible physical mechanisms for phenomenon markets and related fields.

In this paper, a simple and constructive method is presented to find the generalized perturbation (n,M)-fold Darboux transformations (DTs) of modified nonlinear Schrödinger (MNLS) equation in terms fractional forms determinants. particular, we apply (1,N-1)-fold DTs its explicit multi-rogue-wave solutions. The wave structures these rogue-wave solutions MNLS are discussed detail for different parameters, which display abundant interesting structures, including triangle pentagon, etc., may be...

We present a unified theoretical study of the bright solitons governed by self-focusing and defocusing nonlinear Schrödinger (NLS) equations with generalized parity-time- (PT) symmetric Scarff-II potentials. Particularly, PT-symmetric k-wave-number potential multiwell are considered, respectively. For potential, parameter space can be divided into different regions, corresponding to unbroken broken PT symmetry for Kerr nonlinearities. obtained using periodically space-modulated nonlinearity....

We introduce a generalized fractional nonlinear Schrödinger (FNLS) equation for the propagation of optical pulses in laser systems with two fractional-dispersion/diffraction terms, quantified by their Lévy indices, <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msub> <mml:mi>α</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> </mml:msub> <mml:mo> </mml:mo> <mml:mn>2</mml:mn> <mml:mo>∈</mml:mo> <mml:mo stretchy="false">(</mml:mo> <mml:mo>,</mml:mo> stretchy="false">]</mml:mo>...

In this paper, new families of soliton-like solutions are obtained for (2+1)-dimensional integrable Broer-Kaup equations by using the symbolic computation method developed Gao and Tian. Sample from these methods presented. Solitary wave merely a special case in one family. The can also be extended to other types nonlinear evolution mathematical physics.

It is shown that using the similarity transformations, a set of three-dimensional $p\text{\ensuremath{-}}q$ nonlinear Schr\"odinger (NLS) equations with inhomogeneous coefficients can be reduced to one-dimensional stationary NLS equation constant or varying coefficients, thus allowing for obtaining exact localized and periodic wave solutions. In suggested reduction original coordinates in $(1+3)$ space are mapped into one-parametric coordinate surfaces, whose parameter plays role equation....

An integrable system of two-component nonlinear Ablowitz-Ladik equations is used to construct complex rogue-wave (RW) solutions in an explicit form. First, the modulational instability continuous waves studied system. Then, new higher-order discrete RW are found by means a newly derived version generalized Darboux transformation. Finally, perturbed evolution these states explored terms systematic simulations, which demonstrates that tightly and loosely bound RWs are, respectively, nearly...

We analytically study rogue-wave (RW) solutions and rational solitons of an integrable fifth-order nonlinear Schr\"odinger (FONLS) equation with three free parameters. It includes, as particular cases, the usual NLS, Hirota, Lakshmanan-Porsezian-Daniel (LPD) equations. present continuous-wave (CW) conditions for their modulation instability in framework this model. Applying Darboux transformation to CW input, novel first- second-order RW FONLS are found. In particular, trajectories motion...

Higher-order dispersive and nonlinear effects (alias the perturbation terms) such as third-order dispersion, self-steepening, self-frequency shift play important roles in study of ultra-short optical pulse propagation. We consider rogue wave solutions interactions for generalized higher-order Schrödinger (NLS) equation with space- time-modulated parameters. An appropriate transformation is presented to reduce NLS an integrable Hirota constant coefficients. This allows us relate a certain...

The higher order discrete rogue waves (RWs) of the integrable Ablowitz-Ladik equation are reported using a novel version generalized perturbation Darboux transformation. dynamical behaviors strong and weak interactions these RWs analytically numerically discussed, which exhibit abundant wave structures. We show that small noise has weaker effect on strong-interaction than weak-interaction RWs, whose main reason may be related to energy distributions RWs. interaction two first-order is shown...

Abstract Solitons are of the important significant in many fields nonlinear science such as optics, Bose-Einstein condensates, plamas physics, biology, fluid mechanics and etc. The stable solitons have been captured not only theoretically experimentally both linear Schrödinger (NLS) equations presence non-Hermitian potentials since concept parity-time "Equation missing"<!-- image only, no MathML or LaTex -->-symmetry was introduced 1998. In this paper, we present novel bright NLS equation...

We explore the $N_{\infty}$-soliton asymptotics for modified Camassa-Holm (mCH) equation with linear dispersion and boundaries vanishing at infinity: $m_t+(m(u^2-u_x^2)^2)_x+\kappa u_x=0,\quad m=u-u_{xx}$ $\lim_{x\rightarrow \pm \infty }u(x,t)=0$. mainly analyze aggregation state of $N$-soliton solutions mCH expressed by solution Riemann-Hilbert problem in new $(y,t)$-space when discrete spectra are located different regions. Starting from RH problem, we find that i) region is a quadrature...