Painlevé analysis, auto-Bäcklund transformation and analytic solutions of a (2$$+$$1)-dimensional generalized Burgers system with the variable coefficients in a fluid

: It is shown that under certain approximations the basic system of equations governing the propagation of ion acoustic waves can be reduced to the Kortweg-deVries equation. (Author)

On the propagation of ion acoustic solitary waves of small amplitude.

The nonlinear ion-acoustic waves (IAWs) in a space plasma are capable of exhibiting chaotic dynamics which can be applied to cryptography. Dynamical properties of IAWs are examined using the direct method in plasmas composed of positive and negative ions and nonextensive distributed electrons. Applying the wave transformation, the governing equations are deduced into a dynamical system (DS). Supernonlinear and nonlinear periodic IAWs are presented through phase plane analysis. The analytical periodic wave solution for IAW is obtained. Under the influence of an external periodic force, the DS is transformed to a perturbed system. The perturbed DS describes multistability property of IAWs with change of initial conditions. The multistability behavior features coexisting trajectories such as, quasiperiodic, multiperiodic and chaotic trajectories of the perturbed DS. The chaotic feature in the perturbed DS is supported by Lyapunov exponents. This interesting behavior in the windows of chaotic dynamics is exploited to design efficient encryption algorithm. First SHA-512 is used to compute the hash digest of the plain image which is then used to update the initial seed of the chaotic IAWs system. Note that SHA-512 uses one-way function to map input data to the output, consequently it is quite impossible to break the proposed encryption technique. Second DNA coding is used to confuse and diffuse the DNA version of the plain image. The diffused image follows DNA decoding process leading to the cipher image. The security performance is evaluated using some well-known metrics and results indicate that the proposed cryptosystem can resist most of existing cryptanalysis techniques. In addition complexity analysis shows the possibility of practical implementation of the proposed algorithm.

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Dynamical Properties of Ion-Acoustic Waves in Space Plasma and Its Application to Image Encryption

The nonlocal integral elasticity and the modified strain gradient theory are consistently integrated in the framework of the nonlocal modified gradient theory of elasticity. The equivalent differential formulation of the constitutive law, equipped with appropriate nonstandard boundary conditions, is introduced. The size-dependent effects of the dilatation gradient, deviatoric stretch gradient, and symmetric rotation gradient in addition to the nonlocality are beneficially captured in the flexure problem of nano-beams. The well posedness of the proposed nonlocal modified gradient problem is demonstrated via analytical examination of the elastostatic flexure and the wave dispersion phenomenon in nano-beams. The dispersive behavior of flexural waves is verified in comparison with the molecular dynamics simulation. The dominant stiffening effect of the gradient characteristic parameters associated with the nonlocal modified gradient elasticity is confirmed. Both the stiffening and softening responses of nano-structured materials are effectively realized in the framework of the introduced augmented elasticity theory. The conceived nonlocal modified gradient elasticity theory can accordingly provide a practical approach for nanoscopic study of the field quantities.

Contribution of nonlocal integral elasticity to modified strain gradient theory

On the optical soliton solutions of Kundu–Mukherjee–Naskar equation via two different analytical methods

Multistability and dynamical properties of ion-acoustic wave for the nonlinear Schrödinger equation in an electron-ion quantum plasma

Bifurcations of quantum ion-acoustic kink, anti-kink and periodic waves of the Burgers equation are examined in a dense quantum (DQ) plasma comprising of positive ions, electrons and positrons utilizing reductive perturbation technique (RPT) and the concept of dynamical system for the first time. Using RPT and travelling wave transformation, the model equations are converted to a dynamical system. Existence of kink, anti-kink and periodic wave solutions is shown through phase plot and time series plot based on suitable parametric conditions on coefficient of viscosity ($$\eta $$), density ratio of electrons and ions ($$\mu $$) and wave velocity (V). Depending on different parameters, variation of anti-kink, kink and periodic waves is depicted through numerical simulation. The periodic wave of the Burgers equation due to the periodic orbit is offered for the first time in plasmas through Jacobi elliptic function. It is seen that physical parameters $$\eta ,~\mu $$ and V significantly influence amplitude and smoothness of the kink, anti-kink and periodic wave profiles. The output of this contribution may be utilized to interpret the bifurcation behaviour of periodic, kink and anti-kink waves in DQ plasmas with viscosity effect.

Bifurcation analysis of quantum ion-acoustic kink, anti-kink and periodic waves of the Burgers equation in a dense quantum plasma

Bifurcation of quantum electron-acoustic waves (QEAWs) is studied in an adiabatic quantum plasma with nonextensively distributed hot electrons Using reductive perturbation technique, modified Kortweg de Vries (KdV) equation is derived with dual power nonlinearity for highly nonlinear QEAWs Using Galilean transformation the modified KdV equation is reduced to a planar dynamical system with three equilibrium points Applying phase plane analysis periodic wave solutions and supernonlinear periodic wave solutions for QEAWs are perceived It is found that the amplitude of the nonlinear structures is indirectly proportional to the ratio of number densities (
 $$\mu $$
 ), the cold to hot electron temperature ratio (
 $$\sigma $$
 ) and the nonextensivity parameter (q), we have explained physically that confronts our results In addition, coexistence of superperiodic and quasiperiodic phenomena, quasiperiodic and chaotic phenomena and chaotic, superperiodic and quasiperiodic phenomena for QEAWs are observed for appropriate initial values

Characteristics of supernonlinear and coexistence features for electron-acoustic waves in an adiabatic quantum plasma

Investigation of nonlinear dust-acoustic waves (DAWs) in a four-component unmagnetized electron–ion dusty plasma composed of fluid dust species, the Maxwellian positive, and negative ions with $q$ -nonextensive electrons is performed. The dust charge variation is considered for both adiabatic and nonadiabatic cases. For the nonadiabatic case, the Korteweg-de Vries–Burgers (KdV-B) equation is obtained utilizing the reductive perturbation technique (RPT). Implementing the traveling wave transfiguration, the KdV-B equation is transformed into a planar dynamical system (PDS). Implementing the phase plane theory of PDS, qualitative phase portrait profiles of a stable spiral for the corresponding system are presented. The effects of relevant physical parameters are shown on the DAW behavior. Dynamical features, such as quasiperiodic and chaotic motions of the system, are presented via a numerical investigation in the presence of an extraneous periodic force. Sensitivity analysis and the box-counting dimensions for chaotic profiles are presented.

Stable Oscillation and Chaotic Motion of the Dust-Acoustic Waves for the KdV–Burgers Equation in a Four-Component Dusty Plasma

Abstract Multistability and chaotic scenario of arbitrary amplitude ion-acoustic waves in a quantum plasma consisting of negative ions, positive ions and electrons are investigated. The normalized basic equations are transformed to a four dimensional conservative dynamical system by introducing a travelling wave variable. Stability of the fixed points for the corresponding linearized system is briefly examined. Chaotic and quasi-periodic features of the arbitrary amplitude ion-acoustic waves are discussed using effective tools, viz. phase orientations, time series graph and graphs of Lyapunov exponents. Multistability phenomena is established with the help of phase spaces, largest Lyapunov exponents and cross-section of basins of attraction. The chaotic phenomena is further verified by 0−1 test. Results of this study can be applied in understanding dynamical phenomena of arbitrary amplitude ion-acoustic waves in quantum pair-ion plasmas.

Barsha Pradhan

Papers

Multistability and dynamical properties of ion-acoustic wave for the nonlinear Schrödinger equation in an electron-ion quantum plasma

Bifurcation analysis of quantum ion-acoustic kink, anti-kink and periodic waves of the Burgers equation in a dense quantum plasma

Characteristics of supernonlinear and coexistence features for electron-acoustic waves in an adiabatic quantum plasma

Stable Oscillation and Chaotic Motion of the Dust-Acoustic Waves for the KdV–Burgers Equation in a Four-Component Dusty Plasma

Multistability and chaotic scenario in a quantum pair-ion plasma