Space-Curved Resonant Line Solitons in a Generalized (2 + 1)-Dimensional Fifth-Order KdV System

2021 ◽  
Vol 38 (6) ◽  
pp. 060501
Author(s):  
Zequn Qi ◽  
Zhao Zhang ◽  
Biao Li
Keyword(s):  
Resonant Line ◽  
Fifth Order

Three novel fifth-order iterative schemes for solving nonlinear equations

2021 ◽  
Vol 187 ◽  
pp. 282-293
Author(s):  
Chein-Shan Liu ◽  
Essam R. El-Zahar ◽  
Chih-Wen Chang
Keyword(s):  
Nonlinear Equations ◽  
Iterative Schemes ◽  
Fifth Order

scholarly journals Brownian Swarm Dynamics and Burgers’ Equation with Higher Order Dispersion

Symmetry ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 57
Author(s):  
Max-Olivier Hongler
Keyword(s):  
Burgers Equation ◽  
Higher Order ◽  
Underlying Structure ◽  
Swarm Dynamics ◽  
Special Cases ◽  
Kink Waves ◽  
Systematic Derivation ◽  
Fifth Order ◽  
Higher Order Dispersion ◽  
Order Dispersion

The concept of ranked order probability distribution unveils natural probabilistic interpretations for the kink waves (and hence the solitons) solving higher order dispersive Burgers’ type PDEs. Thanks to this underlying structure, it is possible to propose a systematic derivation of exact solutions for PDEs with a quadratic nonlinearity of the Burgers’ type but with arbitrary dispersive orders. As illustrations, we revisit the dissipative Kotrweg de Vries, Kuramoto-Sivashinski, and Kawahara equations (involving third, fourth, and fifth order dispersion dynamics), which in this context appear to be nothing but the simplest special cases of this infinitely rich class of nonlinear evolutions.

scholarly journals RANSAC algorithm for instantaneous frequency estimation and reconstruction of frequency-modulated undersampled signals

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Igor Djurović
Keyword(s):  
Instantaneous Frequency ◽  
Matching Pursuit ◽  
Frequency Estimation ◽  
Consensus Algorithm ◽  
Multidimensional Space ◽  
Instantaneous Frequency Estimation ◽  
Time Frequency ◽  
Polynomial Phase ◽  
Fm Signals ◽  
Fifth Order

AbstractFrequency modulated (FM) signals sampled below the Nyquist rate or with missing samples (nowadays part of wider compressive sensing (CS) framework) are considered. Recently proposed matching pursuit and greedy techniques are inefficient for signals with several phase parameters since they require a search over multidimensional space. An alternative is proposed here based on the random samples consensus algorithm (RANSAC) applied to the instantaneous frequency (IF) estimates obtained from the time-frequency (TF) representation of recordings (undersampled or signal with missing samples). The O’Shea refinement strategy is employed to refine results. The proposed technique is tested against third- and fifth-order polynomial phase signals (PPS) and also for signals corrupted by noise.

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