Invariance properties and conservation laws of the nonlinear damped wave equation with power law nonlinearities

Nonlinear evolution equations represent some of the most fundamental processes in both physics as well engineering. Considering this, we analyze and classify the three dimensional wave equation with a power law nonlinearity in presence of damping and external force terms. In view of the significance of conservation laws in physics, a study of the invariance properties is presented and conservation laws are constructed and classified. An illustrative case of a symmetry reduction in one special case is presented. Keywords: Power law non-linearity, Diffusion, Damped wave, Conservation law

On the Symmetries and Conservation Laws of the Multidimensional Nonlinear Damped Wave Equations

We carry out a classification of Lie symmetries for the (2+1)-dimensional nonlinear damped wave equation utt+fuut=div(gugrad u) with variable damping. Similarity reductions of the equation are performed using the admitted Lie symmetries of the equation and some interesting solutions are presented. Employing the multiplier approach, admitted conservation laws of the equation are constructed for some new, interesting cases

WAO-ARIA consensus on chronic cough - Part II: Phenotypes and mechanisms of abnormal cough presentation — Updates in COVID-19

International audienceBackground: Chronic cough can be triggered by respiratory and non-respiratory tract illnesses originating mainly from the upper and lower airways, and the GI tract (ie, reflux). Recent findings suggest it can also be a prominent feature in obstructive sleep apnea (OSA), laryngeal hyperresponsiveness, and COVID-19. The classification of chronic cough is constantly updated but lacks clear definition. Epidemiological data on the prevalence of chronic cough are informative but highly variable. The underlying mechanism of chronic cough is a neurogenic inflammation of the cough reflex which becomes hypersensitive, thus the term hypersensitive cough reflex (HCR). A current challenge is to decipher how various infectious and inflammatory airway diseases and esophageal reflux, among others, modulate HCR. Objectives: The World Allergy Organization/Allergic Rhinitis and its Impact on Asthma (WAO/ ARIA) Joint Committee on Chronic Cough reviewed the current literature on classification, epidemiology, presenting features, and mechanistic pathways of chronic cough in airway-and reflux-related cough phenotypes, OSA, and COVID-19. The interplay of cough reflex sensitivit

WAO-ARIA consensus on chronic cough - Part II: Phenotypes and mechanisms of abnormal cough presentation — Updates in COVID-19

Background: Chronic cough can be triggered by respiratory and non-respiratory tract illnesses originating mainly from the upper and lower airways, and the GI tract (ie, reflux). Recent findings suggest it can also be a prominent feature in obstructive sleep apnea (OSA), laryngeal hyperresponsiveness, and COVID-19. The classification of chronic cough is constantly updated but lacks clear definition. Epidemiological data on the prevalence of chronic cough are informative but highly variable. The underlying mechanism of chronic cough is a neurogenic inflammation of the cough reflex which becomes hypersensitive, thus the term hypersensitive cough reflex (HCR). A current challenge is to decipher how various infectious and inflammatory airway diseases and esophageal reflux, among others, modulate HCR. Objectives: The World Allergy Organization/Allergic Rhinitis and its Impact on Asthma (WAO/ARIA) Joint Committee on Chronic Cough reviewed the current literature on classification, epidemiology, presenting features, and mechanistic pathways of chronic cough in airway- and reflux-related cough phenotypes, OSA, and COVID-19. The interplay of cough reflex sensitivity with other pathogenic mechanisms inherent to airway and reflux-related inflammatory conditions was also analyzed. Outcomes: Currently, it is difficult to clearly ascertain true prevalence rates in epidemiological studies of chronic cough phenotypes. This is likely due to lack of standardized objective measures needed for cough classification and frequent coexistence of multi-organ cough origins. Notwithstanding, we emphasize the important role of HCR as a mechanistic trigger in airway- and reflux-related cough phenotypes. Other concomitant mechanisms can also modulate HCR, including type2/Th1/Th2 inflammation, presence or absence of deep inspiration-bronchoprotective reflex (lower airways), tissue remodeling, and likely cough plasticity, among others

WAO-ARIA consensus on chronic cough – Part III: Management strategies in primary and cough-specialty care. Updates in COVID-19

International audienceBackground: Chronic cough management necessitates a clear integrated care pathway approach. Primary care physicians initially encounter the majority of chronic cough patients, yet their role in proper management can prove challenging due to limited access to advanced diagnostic testing. A multidisciplinary approach involving otolaryngologists and chest physicians, allergists, and gastroenterologists, among others, is central to the optimal diagnosis and treatment of conditions which underly or worsen cough. These include infectious and inflammatory, upper and lower airway pathologies, or gastro-esophageal reflux. Despite the wide armamentarium of ancillary testing conducted in cough multidisciplinary care, such management can improve cough but seldom resolves it completely. This can be due partly to the limited data on the role of tests (eg, spirometry, exhaled nitric oxide), as well as classical pharmacotherapy conducted in multidisciplinary specialties for chronic cough. Other important factors include presence of multiple concomitant cough trigger mechanisms and the central neuronal complexity of chronic cough

WAO-ARIA consensus on chronic cough - Part III: Management strategies in primary and cough-specialty care. Updates inCOVID-19

Chronic cough management necessitates a clear integrated care pathway approach. Primary care physicians initially encounter the majority of chronic cough patients, yet their role in proper management can prove challenging due to limited access to advanced diagnostic testing. A multidisciplinary approach involving otolaryngologists and chest physicians, allergists, and gastroenterologists, among others, is central to the optimal diagnosis and treatment of conditions which underly or worsen cough. These include infectious and inflammatory, upper and lower airway pathologies, or gastro-esophageal reflux. Despite the wide armamentarium of ancillary testing conducted in cough multidisciplinary care, such management can improve cough but seldom resolves it completely. This can be due partly to the limited data on the role of tests (eg, spirometry, exhaled nitric oxide), as well as classical pharmacotherapy conducted in multidisciplinary specialties for chronic cough. Other important factors include presence of multiple concomitant cough trigger mechanisms and the central neuronal complexity of chronic cough. Subsequent management conducted by cough specialists aims at control of cough refractory to prior interventions and includes cough-specific behavioral counseling and pharmacotherapy with neuromodulators, among others. Preliminary data on the role of neuromodulators in a proof-of-concept manner are encouraging but lack strong evidence on efficacy and safety.The World Allergy Organization (WAO)/Allergic Rhinitis and its Impact on Asthma (ARIA) Joint Committee on Chronic Cough reviewed the recent literature on management of chronic cough in primary, multidisciplinary, and cough-specialty care. Knowledge gaps in diagnostic testing, classical and neuromodulator pharmacotherapy, in addition to behavioral therapy of chronic cough were also analyzed.This third part of the WAO/ARIA consensus on chronic cough suggests a management algorithm of chronic cough in an integrated care pathway approach. Insights into the inherent limitations of multidisciplinary cough diagnostic testing, efficacy and safety of currently available antitussive pharmacotherapy, or the recently recognized behavioral therapy, can significantly improve the standards of care in patients with chronic cough